Enterococcus faecium was isolated in pure culture from several internal organs. The source of infection could be exposure to infected birds or their excrements, as well as contaminated raw poultry meat but, in this case, the source of infection could not be identified.A European Shorthair male cat, neutered, approximately 6 years of age, was presented to the veterinary clinic due to apathy and anorexia. The cat lived mostly outdoors and was fed raw chicken meat. After 3 days of diagnostic procedures and symptomatic treatment, respiratory distress and neurological signs developed and progressed into epileptic seizures, followed by respiratory and cardiac arrest within the next 3 days. Post-mortem examination revealed necrotic lesions in the liver, lungs, and intestines. Notably, the brain displayed perivascular infiltration of lymphocytes and histiocytes. Few foci of neuronal necrosis in the brain were also confirmed. Microscopic examination of the remaining internal organs was unremarkable. The A/H5N1 virus infection was confirmed using a one-step real-time reverse transcription polymerase chain reaction (RT-qPCR). The disease caused severe neurological and respiratory signs, evidence of consolidations and the presence of numerous B lines, which were detected on lung ultrasound examination; the postmortem findings and detection of A/H5N1 viral RNA in multiple tissues indicated a generalized A/H5N1 virus infection. Moreover, a multidrug-resistant strain of  Until a few decades ago, influenza was scarcely diagnosed in cats. However, increasing evidence indicates that several mammalian species, including cats, can be involved in the global circulation of type A influenza viruses (IAVs) . Most fehttps://www.wetgiw.gov.pl/nadzor-weterynaryjny/hpai, accessed on 27 August 2023) before the country was declared HPAI free on 2 August . In Europe, between 3 December 2022 and 23 June 2023, there was a notable presence of HPAI clade 2.3.4.4b. outbreaks in domestic (726) and wild (2382) birds across 25 countries. It appears that there has been a decline in the frequency of disease outbreaks; however, a full comparison is not currently possible due to the ongoing 2022/2023 season [Since 2003, the A/H5N1 virus has caused countless outbreaks of HPAI, initially devastating poultry farming in Southeast Asia, and then spreading to Europe, Africa, and eventually to the Americas . During 3 season ,17,18.https://bnonews.com/index.php/2023/04/another-cat-in-the-u-s-dies-of-h5n1-bird-flu/, accessed on 27 August 2023). In addition, subclinical A/H5N1 infections were identified in three cats in a shelter in Austria [Very rarely, the A/H5N1 virus can infect mammals, including domestic or wild cats ,20,21. D Austria . Moreove Austria ,30.https://www.wetgiw.gov.pl/main/komunikaty/Komunikat-VII-GLW-w-sprawie-choroby-kotow/idn:2302, accessed on 27 August 2023). This countrywide phenomenon, involving both outdoor and indoor cats, was exacerbated by rapid disease progression, limited diagnostic access, lack of established management guidelines and, finally, by a media-fueled panic.In contrast to these sporadic feline cases, in June 2023, veterinary practitioners in various regions of Poland concurrently reported a number of cases of an acute, severe and highly fatal pneumonic disease with neurological signs in cats. At the time of writing, the A/H5N1 virus infection has been confirmed in 33 domestic cats and one captive caracal in Poland  and butorphanol . Ultrasound examination of the lungs and heart was performed using a Versana Premier, GE Medival System  with a 12L-RS linear probe (frequency 10 MHz) and a microconvex 8C-RS ultrasound probe (8 MHz for the heart). X-ray examination of the chest was performed in two projections using an Ecoray-1060HF Portable X-ray Generator .The anatomopathological examination was performed on a fresh carcass. The necropsy was conducted according to standard procedures. Tissue fragments from the brain, lung, heart, liver, spleen, pancreas, kidney, mesenteric lymph node, and intestine were collected and fixed in a phosphate buffered 4% formalin solution for histopathological examination. Then, samples were rinsed in running water, dehydrated in grades of ethanol and xylene, and embedded in paraffin. Paraffin blocks were cut into 4 µm slices, stained with hematoxylin–eosin and examined using the light microscope .Tissue samples from the brain, lung, heart, liver, spleen, pancreas, kidney, mesenteric lymph node, and intestine, as well as nasal swabs, were collected post-mortem and tested using standard diagnostic methods. Columbia Agar with 5% sheep blood, MacConkey agar, Schaedler Agar with 5% sheep blood and Schaedler broth  were inoculated and incubated under aerobic, microaerophilic, and anaerobic conditions at 35.5 °C.Identification of the isolates was performed by 16S rDNA sequencing .Antimicrobial susceptibility was tested using a disk diffusion method in accordance with the CLSI guidelines .Samples for virological examination were collected post-mortem.®  test for the orthomyxovirus type A antigen.Initial screening of the nasal swab was performed using the FluorecareCq) of ≤ 35.00 were considered positive.In order to detect antibodies to the feline immunodeficiency virus (FIV) and feline leukemia virus (FeLV) antigen serum samples were tested using the FIV Ab/FeLV Ag Combo Test .Next, molecular diagnostics for SARS-CoV-2, IAV subtypes H1N1, H3N2, H5N1, and influenza virus type B (IBV) were performed. RNA was extracted from approximately 50 mg of each: lung, brain, spleen, liver, intestine, pancreas, heart, kidney, and mesenteric lymph node samples using a Total RNA Mini Kit , according to the manufacturer’s instructions. One-step reverse transcription real-time PCR (RT-qPCR) was performed using the CFx96 system . Tests for SARS-CoV-2 were conducted with a commercially available Novel Coronavirus (COVID-19) Real Time Multiplex RT-PCR Kit , and with an in-house method described by Stefańska et al. for IAVs . RT-qPCRUpon clinical examination, a fever of 40.5 °C, tachycardia, and mild dehydration were noted. Mucous membranes were pink and superficial lymph nodes were normal in size. No pathological crackles or murmurs were detected on auscultation. A tentative diagnosis of an upper respiratory tract infection was made and a combination of enrofloxacin  and tolfenamic acid  was administered. On the third day of treatment (19 June 2023), the cat’s condition deteriorated, and the patient was admitted to a 24 h veterinary clinic. The symptoms included fast and laborious breathing (100 breaths per minute), hypothermia , and tremors. The cat was placed in an oxygen cage with constant external heating. The treatment with enrofloxacin was maintained and supplemented with ceftriaxone , meloxicam , and intravenous fluid therapy consisting of Ringer’s solution 50 mL/kg b.w./day with potassium chloride  0.5 mEq/kg b.w./h, and a hepatoprotective drug containing ornithine .On the next day, generalized tremors, anisocoria (left pupil more dilated), and hypersensitivity to auditory, visual, and tactile stimuli developed. The cat gradually became semiconscious and began to drool. Subsequently, it experienced epileptic seizures, followed by respiratory and cardiac arrest and death (early morning of 21 June 2023).Meanwhile, the owner reported that two other cats from the same cattery also died during this time, displaying severe dyspnea.Blood tests revealed a considerable increase of activity of aspartate aminotransferase , alanine aminotransferase , creatine kinase , and lactate dehydrogenase , increased total bilirubin concentration , and hypokalemia  accompanied by only mild hypernatremia  and hyperchloremia .Hematological analysis was unremarkable except for a mild shift towards neutrophils in the differential leukogram: white blood cell count 14 G/L (RI: 5.5–19 G/L), red blood cell count 10.9 T/L (RI: 5–10 T/L), hemoglobin concentration 13.7 g/dL (RI: 9–15 g/dL), hematocrit 43% (RI: 28%–45%), platelet count 185 G/L (RI: 180–550 G/L), neutrophils 81% (RI: 50%–75%), lymphocytes 12% (RI: 20%–50%), monocytes 1% (RI: ≤4%), eosinophils 1% (RI: ≤6%), and basophils 5% (RI: ≤4%).The chest radiographs showed bilateral parenchymal densities in the anterior and middle lung fields . UltrasoNecropsy revealed hyperemia of many internal organs.Microscopically, the most obvious lesions were present in the liver, lungs, intestine wall, and brain.The liver displayed presence of numerous foci of necrosis, which were distributed in the whole organ A, while In the lungs, atelectasis, hyperemia, interstitial and interalveolar hemorrhages with multifocal edema, and proteinaceous material in some alveoli were seen A. FurtheNecrotic and inflammatory lesions in myenteric plexuses of the small intestine were observed, characterized by vacuolization and necrosis of the ganglion cells as well as infiltration with lymphocytes and histocytes A,B.The brain displayed perivascular infiltrates of lymphocytes with few histiocytes in the white and grey matter A and theMicroscopic examination of samples of the remaining internal organs was unremarkable and did not reveal the presence of bacteria.Enterococcus faecium by 16S rDNA sequencing. The isolates were resistant to all antimicrobials tested: penicillin, amoxicillin-clavulanate, erythromycin, tetracycline, florfenicol, and enrofloxacin.Pure cultures of abundant bacteria were obtained from the liver, kidney, lymph node, intestine, heart, and lung samples, as well as from the nasal swabs. Single colonies were cultured from the spleen and brain samples. No bacteria were found in the pancreatic tissue. Isolates from all samples were identified as ®–Milapharm test revealed orthomyxovirus type A antigen in the nasal swab.The FluorecareUsing RT-qPCR, samples from the lungs, liver, spleen, intestine wall, and mesenteric lymph node were found positive for A/H5N1 virus RNA, whereas samples from the brain, pancreas, heart, and kidney were negative. Exact results of the influenza A/H5N1 virus RT-qPCR are shown in This case report provides the clinical description, along with pathological, virological, and bacteriological results of feline influenza A/H5N1 case, one of the series observed this summer in Poland. Meanwhile, in some other cats from this cluster of cases, A/H5N1 avian influenza was also confirmed, and the virus was characterized as belonging to the clade 2.3.4.4.b with mutations indicating a mammalian spread ,32. In oIn the blood, significantly elevated activities of AST, ALT, CK, and LDH indicated considerable hepatocyte damage and potential muscle injury. Such increases suggest cytopathic effects induced by the virus, consistent with what one would expect from a A/H5N1 virus infection, as it is known that this agent has a broad cellular tropism. The increased total bilirubin level further confirms liver dysfunction or injury. Elevated red blood cell count combined with a hematocrit approaching the upper limit of the reference range may point to hemoconcentration, which can be attributed to dehydration or other secondary causes. Neutrophilia, with a corresponding decrease in the percentage of lymphocytes, indicates a systemic inflammatory response, commonly seen in viral infections. While these alterations are not unique to the A/H5N1 virus infection, they provide profound insight into the severity and systemic nature of this disease in cats.E. faecium was cultured, while in the histopathological examination using hematoxylin and eosin staining, bacteria were not visualized. This discrepancy could be attributed to the limitations of the staining method, as well as to the distribution of bacteria that might not have been captured within the analyzed tissue sections. Pulmonary and brain lesions mirrored those observed in cats intratracheally inoculated with the IAV A/Vietnam/1194/2004 (A/H5N1), and the lesions in the intestinal plexuses resembled those observed after experimental alimentary infection. The initial testing for the orthomyxovirus type A antigen in the nasal swab proved positive, and post-mortem molecular investigation detected the RNA of the A/H5N1 virus in multiple organs but not in the brain. A possible explanation for the pathological changes in the brain, concurrent with the absence of virus detection, may indicate that the viral load in this tissue was too low to be detected, yet still sufficient enough to induce pathological alterations.The post-mortem examination of the cat revealed non-specific lesions indicative of acute circulatory insufficiency. Histopathological examination showed lesions in several internal organs, predominantly in the lungs, brain, liver, and intestinal wall. While these findings offer valuable insights into the extent of tissue involvement, it is important to emphasize that reaching a definitive diagnosis based on histopathology might not be possible. In the microbiological examination, E. faecium in almost all tested organs suggests secondary septicemia, a common complication of generalized viral infections. E. faecium is a bacterium that naturally colonizes the gastrointestinal tract of cats. Recently, an increased resistance to antibiotics, such as ampicillin and vancomycin, has been observed in some stains [E. faecium infections were responsible for the emergence of the pathological symptoms in this case.The detection of e stains ,35. While stains ,37. The https://www.wetgiw.gov.pl/nadzor-weterynaryjny/hpai, accessed on 14 July 2023). Given that the onset of the disease in the cat occurred almost one month later, and considering that the incubation period for experimental feline infections is approximately 1–2 days, this route of infection seems unlikely. However, it cannot be entirely ruled out, as on 12 June, four days before the first visit of our patient, A/H5N1 infection was confirmed in wild birds in two distant places, both about 200 km from Warsaw . Even if such a distance seems to be a barrier for sick birds, subclinically infected ones could potentially carry the infection to distant areas undetected. Another potential, even though unconfirmed source of infection, could be the diet containing raw poultry products. The risk of such an event has been assessed in the past. A study by Golden et al. [The source of the infection for the investigated cat remains unknown. The most common routes for cats to contract avian influenza virus appear to be direct contact with infected birds, consumption of raw poultry products, or hunting wild birds. These factors naturally put outdoor cats at higher risk. Our patient had outdoor access, and the A/H5N1 virus has been circulating in the wild bird population in Poland for quite some time. However, the last instances of A/H5N1 influenza in wild birds in the central Masovian Voivodeship, where the cat resided, were documented on 22 May 2023 in four dead black-headed gulls . However, feline A/H5N1 infections raise concerns that adaptation of avian viruses to cats—animals living in close contact with humans, and hunting birds—could represent the first step towards potential human-to-human transmission of HPAIVs, potentially resulting in a new pandemic. The clade 2.3.4.4b is linked to the Gs/Gd H5N1 influenza virus as a progenitor, with genetic mutations and adaptations over time leading to the emergence of the latter. This evolutionary process involved changes in the viral genome which contribute to alterations in various aspects of the virus, including its virulence, host specificity, and potential for replication among different species [On very rare occasions, HPAIVs can infect humans and induce a severe disease with high mortality. Since the emergence of the A/H5N1 virus in 1996, approximately 870 human cases resulting from contact with birds have been registered worldwide . Notably, the risk is constantly evaluated and managed within a rigorous legal framework. Specifically, governmental bodies, in the context of mitigating risks associated with HPAI, operate under guidelines delineated in Commission Delegated Regulation (EU) 2020/687, dated 17 December 2019. This serves as a supplementary document to the Regulation (EU) 2016/429 of the European Parliament and of the Council, laying out specific provisions for the prevention and containment of select diseases. In Poland, these guidelines are further specified through a ministerial directive, issued on 23 March 2023, which introduces the ‘National Program for the Detection of Avian Influenza Virus Infections in Poultry and Wild Birds’ for the calendar year 2023 . This cohesive regulatory structure underscores the commitment of governmental agencies to safeguard both public and animal health through evidence-based policy measures.As for now, there have been no documented cases of human infections with the A/H5N1 virus stemming from contact with infected cats, despite the proximity between these animals and their caregivers. Current assessments indicate a low risk of human infection in the general population, and a low-to-moderate risk among individuals in close contact with cats. The World Health Organization has emphasized that this risk could evolve due to viral mutations (


Calidris pusilla) and spotted sandpiper (Actitis macularius). Three time points throughout the year were selected to understand the importance of longitudinal surveys in the characterization of the virome. We finally revisited evidence that upstream and downstream regulation of the inflammatory response is, respectively, associated with resistance and tolerance to viral infections.Normally, the host immunological response to viral infection is coordinated to restore homeostasis and protect the individual from possible tissue damage. The two major approaches are adopted by the host to deal with the pathogen: resistance or tolerance. The nature of the responses often differs between species and between individuals of the same species. Resistance includes innate and adaptive immune responses to control virus replication. Disease tolerance relies on the immune response allowing the coexistence of infections in the host with minimal or no clinical signs, while maintaining sufficient viral replication for transmission. Here, we compared the virome of bats, rodents and migratory birds and the molecular mechanisms underlying symptomatic and asymptomatic disease progression. We also explore the influence of the host physiology and environmental influences on RNA virus expression and how it impacts on the whole brain transcriptome of seemingly healthy semipalmated sandpiper ( Globallirus/and , particuirus/and –10.Arguably, the extent the pandemic was controlled by the administration of non-replicating RNA-vaccines that were designed to induce immunoprotection in survivors –14.If the ongoing pandemic could have been anticipated, few scientists would have expected the magnitude and speed of its spread  or the nThe Pandemic has encouraged government throughout the world to prepare public health policies to anticipate zoonotic diseases and those transmitted by arthropods, the main causes of worldwide outbreaks . OngoingUnderstanding interspecies viral transmission and the ability to model the environmental factors that contribute to the spread of viral diseases to humans is central to the prevention of future pandemics . To begi2In the wild, an enormous number of viral species circulate in specific niches and very little is known about their biology and transmission –39. ManyIn a viral ‘reservoir’ species there is normally an organized immunological response to the virus, but often there is no apparent disease activity –46. In t2.1The pandemic placed bat immunology in the spotlight and it has been suggested that further detailed study may help prevent future pandemics . Bats haBats may  become sick when infected by certain viral species, and the spread of new pathogens into bat colonies be fatal for them . HoweverHerpesviridae, Papillomaviridae, Retroviridae, Adenoviridae and Astroviridae . Many reads related to other families were also found and included Circoviridae, Paramyxoviridae, Coronaviridae, Caliciviridae, Polyomaviridae, Rhabdoviridae, Hepeviridae, Bunyaviridae, Reoviridae, Flaviviridae and Picornaviridae, and the subfamily Parvovirinae. These authors identified in the swabs of a few genera, Rhinolophus spp. Miniopterus spp., and Myotis spp., 16, 10 and 13 virus families respectively, suggesting that these three genera are the major reservoirs for mammalian viruses in China  or Ebola virus followed by mRNA expression analysis, revealed the concentration of virus transcripts in the liver and many transcriptional changes in multiple tissues . These tin China .These data confirmed previous findings that bats are indeed unique reservoirs of diverse virus with immune tolerance , 61, 68.Pseudogymnoascus destructans has been shown to cause infection and high mortality in colonies associated with white nose syndrome  and multiple fowl adenoviruses, with a higher abundance of the last two virus species in the liver . Many otDifferential host responses to avian influenza viruses in avian species with differing susceptibilities were analyzed by transcriptomics, and susceptible birds showed strong neuro-inflammatory responses associated with greater viral load . Ducks aComparative analysis of chickens and ducks following high pathogenic avian influenza virus infection was associated with increased proinflammatory responses in chickens whereas downregulation of inflammatory response in ducks was associated with mild or asymptomatic profiles . In line2.3Rodentia is the most diverse order of mammals, representing more than 40% of mammalian species including 33 families and 2,600 species . They arin vivo infection with the influenza virus  gene deletion (obtained in the knock-out line on a C57BL/6J background) was associated with greater susceptibility to H1N1 infection with significant body weight losses and increased mortality compared to wild controls  mediate human-to-human transmission  , 148. SeVector-borne viruses enter the vector, infect, and replicate. Escaping from the gut and reaching the salivary glands, they infect vertebrate host through saliva during blood feeding , 159. Si3Human pathogens often originate from other species that act as reservoirs/hosts and from where eventual spillover and sustained human-to-human transmission takes place . Indeed,To identify the intermediate host from where viruses may spillover, pathogen screening of animals, animal products and their movements as well as diagnostic of emerging infectious disease is required along the human-wildlife interface , 162. InCalidris pusilla and Actitis macularius) has provided an exciting opportunity to explore phenotypic variations influencing host physiology and environmental factors on the virome. The semipalmated sandpiper (C. pusilla) leaves the Bay of Fundy in Canada and arrives on the coast of South America 5-6 days later in a single non-stop flight with no opportunity to feed .Virome descriptions are generally based on cross-sectional space-time sampling limited to a single time point , 167, th to feed . While tWe compared differential gene expression of viral species quantifying virus transcripts in the brain of different individuals of these trans-oceanic and trans-continental overland long-distance migratory birds. All individuals were captured within three-time windows of the wintering period. Four birds were collected between September and October (recently arrived birds), four between April and May (pre-migratory birds) and four in the intermediate time window (wintering birds). All birds were collected in Otelina Island (0°45’42.57”S and 46°55’51.86”W), in the mangrove area of the Amazon estuary at Bragança municipality, Brazil.Calidris pugnax (Accession code ASM143184v1) followed by NCBI Ref-Seq Viral Genomes (We searched for virus transcripts using the pipeline VIRTUS (v.1.2.1) and VIRTUS2 (v.2.0) using as reference the genome and transcriptome of  Genomes .C. pusilla and A. macularius telencephalon transcriptomes (FASTQ files) subjected to VIRTUS 2 (v.2.0) pipeline, revealed the presence of 370 and 626 virus species respectively  , 99 or aWhen the pathogen is a virus species, its early detection in host cells is accompanied by activation of antiviral effector mechanisms, including type I IFN production , 182, naBats, as other eutherian mammals, synthesize anti-viral effector molecules including type I IFN, T and B cell responses, and innate responses to pathogen-associated molecular patterns (PAMPs) derived from viruses, bacteria or parasites , 187. RNThe IFN system provides the first line of defense against viral infection in vertebrates with type I IFN promoting humoral immunity  and bothInnate lymphocytes , including innate lymphoid cells, natural killer cells, ɣδ T cells and mucosal-associated invariant T cells , were deRousettus aegyptiacus (Marburg virus reservoir) demonstrated the differential expansion of NK cell receptors, MHC class I genes, and type I IFN, as compared to other mammals, suggesting an inhibitory immune state (tolerance), rather than enhanced antiviral defenses (resistance) in bat immune system  when stimulated with polycytidylic acid, Poly (I:C) (ligand of toll-like receptor 3 – TLR3) mimicking a virus infection, or lipopolysaccharides from bacterial membrane (ligands of toll-like receptor 4 - TLR4) showed high levels of mRNA of IFNβ, tumor necrosis factor (TNF) and IL-1β. However, the bats exhibited sustained high-level transcription of the anti-inflammatory cytokine IL-10, which was not detected in the house mouse . As a consequence, the release of budding virions from infected cells may be inhibited –201 that4.1More than two years after its emergence, the SARS-CoV-2 virus continues to affect a subgroup of patients. These patients, who have recovered from the acute phase of the disease, report a diverse repertoire of symptoms that characterize chronic or long COVID-19 , 205. Duvia classical TL receptor inflammatory pathway and this event is crucial for the onset of acute and chronic neuroinflammation and sickness-related behavior , has been linked to both viral-induced and age-related inflammation . Inflamm4.2.2Virus species must introduce their RNA or DNA genomes into the infected cell to replicate, and a number of nuclei acid sensors  includinFrequent spillover of animal influenza viruses to humans, including, swine influenza viruses  and aviaBirds are important reservoirs for RNA viruses and the innate defense against RNA viruses in birds involves detection of viral RNA including RIG-1 receptors, endosomal TLRs and their downstream adaptor proteins . AquaticAlthough RIG-I is involved mainly in antiviral signaling activated by RNA viruses, DNA virus infections (e.g. duck virus enteritis virus) may also increase the expression of IFN- β and RIG-I . RIG-I iRIG-I and MDA5 (melanoma differentiation-associated gene 5), collectively known as RLRs, differentially recognized viral double-stranded RNA virus. For example, RIG-I seems to be essential for IFNs production in response to paramyxoviruses , influenBecause of the bat immune system has the ability to clear or maintain a number of viral infections without apparent clinical signs, bat cell lines have been used to characterize the IFN response to different viral infections in bat reservoirs , 250–2534.2.3IFNs act as extracellular cytokines activating cell surface receptors followed by intracellular kinase signal transduction and phosphorylation of transcription factors leading to the induction of ISGs allowing antiviral defense, antiproliferative activities, and stimulation of adaptive immunity . All typInfectious bronchitis virus (IBV) is a single strand, positive sense RNA virus (belonging to gammacoronaviruses)  that indThe host innate immune response mediated by IFN-1 results in the up-regulation of hundreds of ISGs and provides early protection against viral infection. Comparative studies have revealed that while many ISGs are common to all mammals, each species displays its own distinct repertoire of ISGs . AntivirHipposideros armiger) transplanted into H1N1 infected mice, reduces the inflammatory response and increases survival rate being that associated with increased production of flavonoid and isoflavones as well as with the quick innate immune response induced by the bat fecal transplanted microbiota, thus conferring mouse tolerance to influenza virus (H1N1) infection  while also inhibits antiviral and antiproliferative responses induced by IFN-I. Consistent with this, SOCS1 ablated cells and SOCS1−/− mice are resistant to viral infection ; 275. Sinfection .To obtainfection , 289. Fonfection –292.5Few scientists would have expected the magnitude and speed of the spread of the COVID-19 pandemic. While the deaths, rightly, have attracted the headlines, an unknown number of carriers of post-acute sequelae of SARS-CoV-2 still require medical attention. To anticipate pandemics in the future and avoid unnecessary morbidity and mortality, it has been suggested that a broader characterization of the animal virome, host physiology and the underlying mechanisms associated with disease tolerance and anti-viral defenses are essential. We reviewed the literature concerning the virome of bats, rodents and migratory birds and highlighted the potential mechanisms of tolerance and resistance to virus infection in these groups. It is now clear that the type of host inflammatory response to the presence of virus is central to these mechanisms. We also emphasize the importance of understanding and controlling the dysfunctional innate immune system and inflammasome to deal with future outbreaks in the period before we have effective vaccines.CD, CG-D, PP, DD, NM and MM contributed to conception and design of the study. PP organized the database and performed statistical analysis. DD optimized figures and adapted submission to the journal requirements. CD wrote the first draft. DB wrote section of the manuscript. CD, DA, DD and DB contributed to final edition. All authors contributed to the article and approved the submitted version.


The paper focuses on the computing paradigm of virus machines within the area of Unconventional Computing and Natural Computing. Virus machines, which incorporate concepts of virology and computer science, are considered as number computing devices with the environment. The paper designs a virus machine that solves a generalization of the semiprime factorization problem and verifies it formally.The security that resides in the  Natural computing1, a branch of Unconventional computation inspired by what occurs in nature, has gained significant traction with the emergence of neural networks, cellular automata, membrane computing, etc.In recent years, surpassing the computational capacity of today’s computers has become a major goal in the digital world. As a result, researchers have turned to unconventional models to revolutionize problem-solving approaches. 2.In the vast field of virology, a virus stands as a diminutive yet potent infectious agent that crucially relies on infiltrating a host cell to perpetuate its reproductive cycle. With astonishing versatility, viruses showcase their ability to infiltrate not only animals but also plants and protist species, thus affirming their ubiquity within the intricate tapestry of the natural world. A staggering estimation postulates the coexistence of approximately 350 trillion viruses, a colossal quantity that surpasses the number of bacteria and cells by an astounding factor of 10. As the COVID-19 pandemic permeated society, the scientific community, as well as the populace at large, bore witness to the devastating capabilities harboured within the realm of viruses. Such pervasive prevalence inherently instigates an intellectual curiosity that beckons the exploration of the intricately woven computational aspects underlying this captivating biological structure, for more detail information we refer tovirus machines3 has garnered attention. Inspired by the movement and replication behaviour of viruses within hosts, virus machines utilize an instruction graph to navigate and replicate itself through different channels within a system. Virus Machines have been studied as function computing mode, recognizer mode, and generating mode.Within the branch of unconventional computing, a promising and young model called 3. In addition, it seems to be useful to solve mathematical problems in a numerical point of view, authors in4 computed an arithmetic calculator and two pairing functions by virus machines. Finally, authors in5 opened a computational complexity theory through these devices.This computing paradigm is universal (as powerful as turing machines) when there is no bounded restrictions on the number of hosts, instructions and viruses in the hostCryptography is a scientific discipline that concerns the security of the information in the presence of possible intruders, as well as authentication and identification, providing privacy and integrity. There are cryptosystems where the issuer has both a public and a private key to encrypt and decrypt , within asymmetric cryptography, highlights the public-key cryptosystems. The first published public key cryptosystem, named RSA, was established by Rivest et al.6.RSA cryptosystem. In “semiprime factorization problem. The paper ends with some open problems and concluding remarks.The paper is organized as follows. Next section briefly describes different versions of the integer factorization problems, and the next section to it is devoted to the integer factorization problem is the following: given a natural number greater than 1, find its prime factorization. It is conjectured to be a computationally hard problem. A decision version of this problem is the semiprime factor problem that can be described as follows: given two natural numbers x, y greater than 1, determine whether or not x has a factor less than y. This problem belongs to the complexity classes NP, co-NP and BPQ7. It is interesting to notice that if that problem is NP-complete or co-NP-complete then NPco-NP, for further information we refer to8.The semiprime factorization problem is the least prime divisor (LPD): “Given a natural number m is a divisor of n”. Obviously, such m must be a prime number. This problem can be characterized by the partial function m is least divisor of n greater than 2. Throughout this paper, a deterministic virus machine solving the least prime divisor problem . In fact, it has not been proven that the existence of an efficient algorithm for factoring large semiprimes is not possible. Nevertheless, some pathways have been studied with other unconventional computing models, such as quantum computation, which highlights recent works in the benefits of quantum communication or the combination of quantum communication with classical cryptography12.The n for RSA is used as the modulus for both public and private keys. In order to attack the RSA system, the factorization of n is needed. Many systems, such as banks, medical databases and critical systems with confidential information, keep their data secure thanks to this method. It is interesting to highlight the inherent asymmetry between generating large semiprimes and factoring them.Any large semiprime input 3. Next, the syntax of this paradigm is formally defined.This young computing paradigm, inspired by the way viruses are transmitted and replicated between hosts, was first introduced inp, q), I with, at most, an arc from j, A virus machine  of degree , is a tuple that can be viewed as an ordered set of phosts labelled as viruses, and an ordered set of qcontrol instruction units labelled with output region, denoted by transmission channels through which viruses can transmit from one host activated: if a instruction t, then it will be opened and one virus will be transmitted and replicated closed.Formally, a instruction paths that will follow the computation, and they have associated with a weight. Finally, the undirected bipartite graph instruction-channel relation by which an edge Arcs from the directed graph weight (or weight 1 if it is not marked). The instruction-channel arcs are represented as dotted red lines.Graphically, an example of virus machine of degree , can be viewed in Fig. semantics are then described as follows: a configurationinstant description at an instant t of a virus machine is a tuple initial configuration of a system transition step, denoted by Assuming that the control instruction unit out-degree of out-degree of If out-If If there is no possible path, then Object A computation of a virus machine is a (finite or infinite) sequence of configurations such that: (a) the first term is the initial configuration n-th term of the sequence is obtained from the previous term in one transition step; and (c) if it is a halting computation (the sequence is finite) then the last term is a halting configuration.The sequential devices, that is, in any instant at most a control instruction unit is activated and, hence, at most one transmission channel will be opened.Virus machines are p, q).r input hosts and A virus machine with input, of degree p, q, r) and initial configuration of with inputIf Next, virus machines providing function computing devices, is introduced.k input hosts, if for each z.If If We say that a partial function 5, is presented. Let For a better understanding in the behavior of these devices, a basic example fromThe VM entclass1pt{minimaa:if If Note that for all values of a, the configuration is a and b.Given an input least prime divisor problem by using virus machines, it suffices to design such a machine that computes the partial function In order to solve the From now on, since the description of a single virus machine can be tedious to read, it is easy to depict them with graphics and setting that Let us consider the VM A method to formally verify that a computational device of a model solves a given problem is to find invariant formulas in some relevant loops of the device, in such a way that the veracity of those formulas at the end of the loops provides relevant information.least prime divisor problem, that is, we must prove mathematically that the designed virus machine computes the partial function Next, we give a sketch of a virus machine with respect to the n and j, and For every Let Finally, let us consider the following formula:Let us suppose that This formula is an invariant of the machine, and by induction we get the following proposition.From Proposition n is a prime number and to show that it is of quadratic order.Formal verification also results in a useful tool for studying the time complexity of a device as we know exactly the number of the steps necessary for the machine halts. From Remark 4 in Appendix A, we can conclude that the time complexity of this machine belongs to the quadratic order RSA) lies in the presumed intractability of the semiprime problem, from a computational complexity point of view. This problem is characterized by the partial function m is least prime divisor of n. Throughout this paper, a deterministic virus machine solving the least prime divisor, has been designed and the formal verification of it is proved. Despite of the lack of efficiency that should be improved, these devices gives an interesting scope for solving numerical problems thanks to the mathematical integrity of the formal verification and its easy study of time complexity.The security of the first public-key cryptosystem (Furthermore, while the concept of virus machines is relatively new, there are numerous unexplored avenues within this field. Currently, the lack of efficiency of virus machines is because of its sequential behavior, and exploring parallelism could potentially enhance this aspect. Future research directions could involve expanding the model to incorporate additional biological aspects, deepening our understanding of virus functionality and exploring potential applications. Establishing connections between virus machines and traditional virology is also an intriguing area for exploration. Finally, while improvements in efficiency are studied, we believe that a specific hardware implementation could figure out an innovative scope.Supplementary Information.


A viral infection can modify the risk to subsequent viral infections via cross‐protective immunity, increased immunopathology, or disease‐driven behavioral change. There is limited understanding of virus–virus interactions due to lack of long‐term population‐level data.Our study leverages passive surveillance data of 10 human acute respiratory viruses from Beijing, Chongqing, Guangzhou, and Shanghai collected during 2009 to 2019: influenza A and B viruses; respiratory syncytial virus A and B; human parainfluenza virus (HPIV), adenovirus, metapneumovirus (HMPV), coronavirus, bocavirus (HBoV), and rhinovirus (HRV). We used a multivariate Bayesian hierarchical model to evaluate correlations in monthly prevalence of test‐positive samples between virus pairs, adjusting for potential confounders.Of 101,643 lab‐tested patients, 33,650 tested positive for any acute respiratory virus, and 4,113 were co‐infected with multiple viruses. After adjusting for intrinsic seasonality, long‐term trends and multiple comparisons, Bayesian multivariate modeling found positive correlations for HPIV/HRV in all cities and for HBoV/HRV and HBoV/HMPV in three cities. Models restricted to children further revealed statistically significant associations for another ten pairs in three of the four cities. In contrast, no consistent correlation across cities was found among adults. Most virus–virus interactions exhibited substantial spatial heterogeneity.There was strong evidence for interactions among common respiratory viruses in highly populated urban settings. Consistent positive interactions across multiple cities were observed in viruses known to typically infect children. Future intervention programs such as development of combination vaccines may consider spatially consistent virus–virus interactions for more effective control. For example, public health interventions such as vaccination campaigns targeting a particular virus may impact the abundance of other viruses competing for or occupying the same niche.Statistical methods are needed to better tease out potential biological interactions between viruses in the presence of confounding socioenvironmental factors associated with virus survival and transmission, such as climatic conditions, age‐dependent contact patterns, and changes in testing frequencies. For example, shared seasonality patterns between influenza and RSV often confound interpretation of temporal correlation between the two viruses. One study in Scotland accounted for these factors via hierarchical autoregressive modeling to examine interactions between multiple groups of respiratory viruses over several years.Herein, we adapt a Bayesian virus–virus interaction framework designed for surveillance data with relatively dense sampling22.1Our data on acute respiratory infections (ARIs) were collected by the Surveillance for Etiology of Respiratory Infections program, an ongoing nationwide passive surveillance program initiated from 2009, which covers 314 sentinel hospitals in all 31 provinces in China. The ARIs were defined as (1) at least one of the following conditions: fever, abnormal white blood cell differentials, leukocytosis or leukopenia; and (2) at least one of the following symptoms/signs: cough, chills, expectoration, nasal congestion, sore throat, chest pain, tachypnea, and abnormal pulmonary breath sounds. In compliance with the standard operating protocol of surveillance developed by China CDC, a random sample of inpatients and outpatients presenting ARIs were enrolled, and nasopharyngeal specimens were collected from enrolled patients prior to any treatment to be tested for the presence of influenza virus , RSV‐A and RSV‐B, HPIV types 1–4, HAdV, HMPV, HCoV, HBoV, and HRV. All viruses were tested by reverse transcription‐polymerase chain reaction (RT‐PCR) except HAdV and HBoV, which were tested by PCR. Details about the laboratory procedures are given elsewhere.We focus on four metro cities that consistently tested patients for these viruses throughout the 11‐year period: Beijing, Chongqing, Guangzhou, and Shanghai. Nearly all enrolled patients presenting with acute respiratory symptoms were tested for all respiratory viruses during 2009–2019. There was a lower testing rate, however, for HRV during 2009–2011, so we restricted analyses related to HRV to 2012–2019. We also excluded influenza C from analysis and grouped HPIV 1–4 viruses into a single HPIV group due to the relatively low frequency of each individual virus. Analyses were done for the total population studied and separately for children <18 years and adults ≥18 years. There was a lower testing rate for adults in Chongqing in 2011 and 2015–2019; therefore, that subgroup was excluded from age‐stratified analyses.2.2p < 0.05 and p < 0.10, with weights corresponding to the number of tests administered. The p values were corrected for multiple comparisons using the Benjamin–Hochberg procedure,q values were reported. Statistical significance was defined as q ≤ 0.10, that is, controlling the FDR at 10%. We also calculated weighted Pearson's coefficients in monthly infection prevalence by sex for each virus in each city. At the individual level, we also calculated the odds of co‐infection for each virus with each of the other viruses (45 virus pairs) in each city and used Fisher's exact test for statistical significance, and similarly, FDR‐adjusted q values were reported.For correlation analyses, we aggregated data into monthly infection counts for each virus to evaluate the population‐level covariation patterns between viruses in each city . We calculated a measure of prevalence of positive tests for each virus as the number of infected patients over the total number of patients tested for each virus for each month. We calculated weighted Pearson's coefficients and 95% confidence intervals (CIs) to evaluate unadjusted correlations in monthly infection prevalence between each of the 45 virus pairs with statistical significance set at 2.3Simple correlations among respiratory viruses may be confounded by changes in testing frequencies, temporal autocorrelation, and other factors. To address these challenges, we used a multivariate Bayesian hierarchical model, adapting an approach initially designed by Mair et al.Before applying the hierarchical model, we smoothed observed monthly infection counts for each virus using logistic regression, adjusting for common risk factors for infection. We fitted generalized linear models for each virus and city, incorporating harmonic functions to account for seasonality and polynomials of year to capture long‐term trends, while also adjusting for sex and age groups.ρ to characterize virus–virus interactions. A range of  for ρ effectively covers a range of  for the correlation coefficient. A fundamental distinction in our model compared with previous workIn the second stage, we modeled interactions between pairs of viruses separately. We introduced a multiplicative random odds ratio (OR) to describe how the realized prevalence of positive samples for each virus deviates from the expected prevalence. This random OR is related to the random effect φ, which follows a multivariate AR (1) structure to capture correlations between viruses. Specifically, we used the correlation coefficient We used 10 chains, each with a burn‐in of 20,000 iterations, followed by 600 thinned draws from 60,000 additional iterations per chain, ensuring convergence Figure . Models 33.1Our dataset included 216,030 patients from January 2009 to December 2019, of whom 115,622 (53.5%) were from Beijing, Chongqing, Guangzhou, and Shanghai, four large metro cities each with a population size of 15–31 million. Of 101,643 patients from the four cities who were tested for any of the viruses of interest, 44.7% were from Beijing, 59.2% were male, and 50.8% were children Table . Of pati3.2There were 33,650/101,643 (33.1%) patients who tested positive for any of the 10 viruses studied Figure , of whomq ≤ 0.10 in Beijing , 30 in Shanghai , 26 in Guangzhou , and 22 in Chongqing  , HPIV and HCoV in Shanghai , HRV and HBoV in Guangzhou , and IBV and RSV‐B in Chongqing .At the individual level, we evaluated for each pair of viruses the OR of co‐infection by city but lumping data from all 11 years, while controlling for FDR ≤ 0.10. Of 45 pairwise tests in each city, 36 were significant at ) Figure . In Beij3.3p ≤ 0.05 and p ≤ 0.1 that are unadjusted for multiple comparisons are shown in Figures p ≤ 0.05. Stratifying by age group, viral correlations for children were largely consistent with the overall population , 12 in Chongqing , 10  in Beijing, and seven in Guangzhou . HPIV was positively correlated with HRV in all four cities with correlations ranging from 0.49 to 0.56   and Chongqing , RSV‐B and HRV in Guangzhou , and HMPV and HRV in Shanghai . Some viruses were interactive with as many as five other viruses in a particular city, for example, IAV in Chongqing and HRV in Shanghai. Using p value ≤0.05 to determine statistical significance but without adjustment for multiple comparisons  Figure . Monthly) Figure  confirmes Figure  yielded l Figure  addition3.6q ≤ 0.10 among adults in Beijing, Guangzhou, and Shanghai, respectively. Chongqing was not examined due to sparsity in the number of tested adults.The Bayesian model fitted solely on children revealed many more significant virus–virus correlations than the total population, 24–29 in each of the four cities Figure . All vir4We assessed potential positive and negative interactions between acute respiratory viral infections among four major cities in China over an 11‐year period, adjusting for demographics, temporal autocorrelations, seasonality, long‐term trends, and multiple comparisons. The data are unique because of not only the coverage of a long time‐span and large metro‐populations but also the simultaneous testing of a comprehensive panel of respiratory viruses from each patient. The most convincing interactions, as shown by both the overall analyses and children‐specific analyses, are the positive correlations between HPIV and HRV and between HBoV and HRV. Although the pair of HBoV and HRV did not reach statistical significance in Shanghai, the direction of association is consistent in all four cities. Equally noticeable is the pair of RSV‐A and HCoV among children, which showed consistent positive associations in all four cities and statistical significance in three. More positive correlations were found than negative correlations, and more associations were found in children than in the general population. There was also a substantial level of spatial heterogeneity in the virus–virus interactions, for example, strong negative correlation of IAV with HRV and HMPV, as well as that between RSV‐A and RSV‐B, were only seen in Chongqing.HPIV was positively correlated with HRV in all cities in Bayesian analyses. HPIVs are one of the most common causes of lower respiratory tract infections among children <5 years, accounting for up to 17% of hospitalizations from pneumonia.HCoV was positively correlated with HPIV in three cities for children in adjusted analyses. We are unaware of other population‐level analyses supporting these findings, but several studies reported increased frequency of co‐infection between HPIV and HCoV‐229E in Shanghai,In adjusted analyses, we observed positive correlations among pairs of viruses including RSV‐B, HBoV, HAdV, and HMPV—viruses that frequently cause lower respiratory tract infections in young children. This is consistent with a 10‐year study in central Europe, which found that HRV/HBoV, HRV/HAdV, RSV/HBoV, RSV/HAdV, RSV/HRV, and RSV/HCoV‐OC43 were the most prevalent co‐infections.Among children, IAV was negatively correlated with HAdV in three cities, and HRV, HBoV, HMPV, and RSV‐B in Chongqing, which is in accord with several studies that reported shifts in the timing and severity of other respiratory infections following IAV epidemics.Most of the statistically significant correlations among respiratory viruses were positive associations, which could result from several factors, including shared transmission routes, interactions with the host immune system, or environmental conditions that favor multiple virus types.There were inconsistencies in virus–virus interactions between adult and child populations, even within the same city. Children and adults have distinct immune responses due to differences in immune system maturity and prior exposure to respiratory viruses.Our study had several limitations. First, we did not assess higher order interactions between three or more viruses. Second, bacterial infections, which were not examined in this study, may also play a mediating role in one's susceptibility to viral co‐infection. Third, 4.9% of patients included in this study were only tested for two viruses of interest (IAV and IBV) during the 2009 H1N1 influenza pandemic, suggesting some co‐infections in those patients might have been missed. Fourth, our study used hospital surveillance data, which includes symptomatic individuals seeking care. Influenza, RSV, and other viral infections may not present clinically, so it is unclear to what extent asymptomatic infections impacted the observed interactions.5Virus–virus interactions may have a significant impact on viral disease severity, transmissibility, immune response, and vaccine effectiveness. Different virus pairings may trigger different pathogenic mechanisms, which could inhibit or amplify clinical and public health consequences. Spatially consistent virus–virus interactions warrant future research to understand their biological pathways and social determinants and may be considered for more effective intervention programs, for example, developing combination vaccines for children. Our method extends the statistical approach designed for dense sampling to sparse sampling to provide insights of virus–virus interactions among four major cities in China over an 11‐year period. The method could be further improved by incorporating individual‐level co‐infection status. The SARS‐CoV‐2 pandemic may pose new challenges on modeling virus–virus interactions. Recent research demonstrates a significant reduction in a broad spectrum of acute respiratory viruses consequent to SARS‐CoV‐2 likely due to the synergy of nonpharmaceutical interventions , reduced testing of seasonal respiratory viruses, and viral interferences.Zachary J. Madewell: Formal analysis; investigation; methodology; software; validation; visualization; writing—original draft; writing—review and editing. Li‐ping Wang: Conceptualization; data curation; funding acquisition; investigation; methodology; project administration; resources; writing—review and editing. Natalie E. Dean: Funding acquisition; investigation; methodology; writing—original draft; writing—review and editing. Hai‐Yang Zhang: Data curation; investigation; methodology; resources; writing—review and editing. Yi‐Fei Wang: Data curation; investigation; methodology; resources; writing—review and editing. Xiao‐Ai Zhang: Data curation; investigation; methodology; resources; writing—review and editing. Wei Liu: Data curation; investigation; methodology; resources; writing—review and editing. Wei‐Zhong Yang: Data curation; funding acquisition; investigation; methodology; resources; writing—review and editing. Ira M. Longini: Funding acquisition; investigation; methodology; writing—review and editing. George F. Gao: Data curation; funding acquisition; investigation; methodology; resources; writing—review and editing. Zhong‐Jie Li: Data curation; funding acquisition; investigation; methodology; resources; writing—review and editing. Li‐Qun Fang: Conceptualization; data curation; funding acquisition; investigation; methodology; project administration; resources; supervision; validation; visualization; writing—review and editing. Yang Yang: Conceptualization; formal analysis; funding acquisition; investigation; methodology; project administration; resources; software; supervision; validation; visualization; writing—original draft; writing—review and editing.The authors declare no conflict of interests.Data collection was considered to be public health surveillance by the National Health Commission of the People's Republic of China and verbal informed consent was obtained from patients or their legal guardians. The surveillance protocol was reviewed and approved by the ethics review committees of the China CDC (2015‐025).https://www.webofscience.com/api/gateway/wos/peer-review/10.1111/irv.13212.The peer review history for this article is available at Figure S1. Example MCMC trace plots of model parameter estimates for the Bayesian hierarchical model for influenza B virus (IBV) and human parainfluenza virus (HPIV) in Beijing.Figure S2. Monthly numbers of laboratory‐tested samples with and without viral infections from January 2009 to December 2019 in four metro cities, China.Figure S3. Monthly percentage of patients diagnosed with a single viral infection, a viral co‐infection, or determined to be virus‐negative from January 2009 to December 2019 in four metro cities, China.Figure S4. Monthly viral prevalence by sex from January 2009 to December 2019 in four metro cities, China. Weighted Pearson's coefficients in monthly infection prevalence between the two sexes for each virus in each city and 95% confidence intervals are shown, with weights corresponding to the number of tests administered by city. Prevalence was the number of infected patients over the total number of patients tested for each virus for each month.Figure S5. The proportion of all tests for each virus that were positive and total number of infections in four metro cities, China. Larger circles represent a greater proportion of positive tests and darker colors represent greater numbers of infections.Figure S6. Number of tests (light) and proportion of tests that were positive (dark) for each acute respiratory virus by age group in four metro cities, China.Figure S7. Relative prevalence of viruses from January 2009 to December 2019 in four metro cities, China.Figure S8. Ratio of odds of infection with one virus between presence vs. absence of the other virus for each virus pair, based on tabulating individual detection data from January 2009 to December 2019 in four metro cities, China. Blue represents odds ratios (OR) > 1, red represents ORs < 1, and larger circles represent smaller q‐values. The q‐values control for false discovery rate and are based on p‐values from the Fisher's exact test.Figure S9. Weighted Pearson's correlation coefficients for the total population studied and 95% confidence intervals of monthly prevalence for each pair of respiratory viruses in four metro cities of China, where weights are the numbers of tests administered. This figure is identical to Figure 3, but with 95% confidence intervals instead of q‐values. Blue and red indicate statistically significant (p < 0.05) positive and negative coefficients, respectively. Green and purple borders indicate virus pairs significant in three and four cities, respectively. The p‐values are not adjusted for multiple comparisons.Figure S10. Weighted Pearson's correlation coefficients for the total population studied and 90% confidence intervals of monthly prevalence for each pair of respiratory viruses in four metro cities of China, where weights are the numbers of tests administered. This figure is identical to Figure 3, but with 90% confidence intervals instead of q‐values. Blue and red indicate statistically significant (p < 0.1) positive and negative coefficients, respectively. Green and purple borders indicate virus pairs significant in three and four cities, respectively. The p‐values are not adjusted for multiple comparisons.Figure S11. Weighted Pearson's correlation coefficients for children <18 years and q‐values of monthly prevalence for each pair of respiratory viruses in four metro cities of China, where weights are the numbers of tests administered. The q‐values represent statistical evidence adjusted for multiple comparisons by controlling the false discovery rate. Significant correlations (q ≤ 0.10) are shown in colour. Blue and red indicate positive and negative coefficients, respectively. Green and purple borders indicate virus pairs statistically significant with consistent directions in three and four cities, respectively.Figure S12. Weighted Pearson's correlation coefficients for adults ≥18 years and q‐values of monthly prevalence for each pair of respiratory viruses in four metro cities of China, where weights are the numbers of tests administered. The q‐values represent statistical evidence adjusted for multiple comparisons by controlling the false discovery rate. Significant correlations (q ≤ 0.10) are shown in colour. Blue and red indicate positive and negative coefficients, respectively. Yellow borders indicate virus pairs statistically significant with consistent directions in two of the three cities, respectively. There was a lower testing rate for adults in Chongqing, therefore that subgroup was not analyzed.Figure S13. The observed and expected prevalence of each virus before applying the multivariate Bayesian hierarchical model, January 2009 to December 2019 in four metro cities, China. The expected prevalence was calculated by fitting generalized linear models for each virus and city with harmonic functions to account for seasonality and polynomials to account for long‐term trends, while adjusting for sex and age group . Prevalence was the number of infected patients over the total number of patients tested for each virus for each month.Figure S14. Monthly prevalence of human parainfluenza virus and human rhinovirus from January 2009 to December 2019 in four metro cities, China. Prevalence was the number of infected patients over the total number of patients tested for each virus for each month.Figure S15. Bayesian hierarchical model correlation coefficients for the total population studied and 95% credible intervals, adjusting for age, sex, seasonality, changes in testing frequency, and autocorrelation. This figure is identical to Figure 4, but with 95% credible intervals instead of q‐values. Blue and red indicate statistically significant (p < 0.05) positive and negative coefficients, respectively. Purple borders indicate virus pairs significant in four cities. The p‐values are not adjusted for multiple comparisons.Figure S16. Bayesian hierarchical model correlation coefficients for the total population studied and 90% credible intervals, adjusting for age, sex, seasonality, changes in testing frequency, and autocorrelation. This figure is identical to Figure 4, but with 90% credible intervals instead of q‐values. Blue and red indicate statistically significant (p < 0.10) positive and negative coefficients, respectively. Green and purple borders indicate virus pairs significant in three and four cities, respectively. The p‐values are not adjusted for multiple comparisons.Figure S17. Bayesian hierarchical model correlation coefficients for children <18 years and q‐values, adjusting for age, sex, seasonality, changes in testing frequency, and autocorrelation. The q‐values represent corrected p‐values for multiple comparisons by controlling the false discovery rate. Significant correlations (q ≤ 0.10) are shown in color. Blue and red indicate positive and negative coefficients, respectively. Green and purple borders indicate virus pairs significant in three and four cities, respectively.Figure S18. Bayesian hierarchical model correlation coefficients for adults ≥18 years and q‐values, adjusting for age, sex, seasonality, changes in testing frequency, and autocorrelation. The q‐values represent statistical evidence adjusted for multiple comparisons by controlling the false discovery rate. Significant correlations (q ≤ 0.10) are shown in colour. Blue and red indicate positive and negative coefficients, respectively. There was a lower testing rate for adults in Chongqing, therefore that subgroup was excluded from this analysis.Table S1. Numbers of viruses tested for each patient (N = 101 643). Viruses tested included: influenza A and B; respiratory syncytial virus A and B; and human parainfluenza virus, adenovirus, metapneumovirus, coronavirus, bocavirus, and rhinovirus.Table S2. Quasi‐Akaike information criteria for harmonic regression models for the total population studied by virus and city. The lowest Quasi‐Akaike information criteria for each model is shown in bold.Table S3. Mean, standard deviation, and quantiles of the marginal posterior distribution for ρ, and convergence diagnostics for Bayesian hierarchical model.Click here for additional data file.


This reduces the costs for hydrogen production to 1.26 €/kg by 2050. Hydrogen production switches from grey to green hydrogen, omitting the option of blue hydrogen. If electrolysis costs are modelled without dynamic learning-by-doing, then the electrolysis scale-up is significantly delayed, while total system costs are overestimated by up to 13% and the levelised cost of hydrogen is overestimated by 67%.Many studies have shown that hydrogen could play a large role in the energy transition for hard-to-electrify sectors, but previous modelling has not included the necessary features to assess its role. They have either left out important sectors of hydrogen demand, ignored the temporal variability in the system or neglected the dynamics of learning effects. We address these limitations and consider learning-by-doing for the full green hydrogen production chain with different climate targets in a detailed European sector-coupled model. Here, we show that in the next 10 years a faster scale-up of electrolysis and renewable capacities than envisaged by the EU in the REPowerEU Plan can be cost-optimal to reach the strictest +1.5 This study highlights the importance of including learning-by-doing for hydrogen production in energy models. It reveals that scaling up renewable capacities and electrolysis faster than the EU’s REPowerEU Plan can be cost-effective under strict climate targets, reducing hydrogen production costs and shifting from grey to green hydrogen. In the future, however, hydrogen produced with low carbon emissions is likely to play an increasing role in the energy mix as decarbonisation progresses with shares of up to 24% of the final energy demand by 20502. Applications could include the production of green steel3 or synthetic fuels5. There are several ways in which hydrogen can be produced: (i) from fossil fuels such as coal or natural gas, (ii) from fossil fuels in combination with CO2 capture, or (iii) via electrolysis. The production costs for hydrogen depend in the first two cases on the price of fossil fuels, and in the second case on the cost of electricity. In order to reduce dependence on fossil fuels with high gas prices and to accelerate the energy transition, the European Commission aims to boost the deployment of hydrogen electrolysis. This objective has been concretised in the REPowerEU plan6 published in May 2022, which has set a goal to produce 10 million tonnes of hydrogen with renewable electricity and to import further 10 million tonnes to the EU by 2030.Today hydrogen plays a minor role in European final energy consumption with a 2% share9 or on expert surveys10. Way et al.8 explore various cost distributions for the world’s energy system up to year 2070 for multiple technologies via a Monte Carlo approach. Through the different investment cost trajectories they cover uncertainties in the cost developments, but the path for installed capacities are exogenously defined and energy dispatch is not modelled.Hydrogen produced from water electrolysis using renewable electricity, so-called green hydrogen, is considered to be crucial to decarbonise hard-to-electrify sectors of the energy system. Since it is an immature technology, it is highly likely that costs and efficiencies will improve as production scales up, a phenomenon known as ‘learning-by-doing’. Several studies have been carried out on how future hydrogen electrolysis investment costs develop over time or with capacity deployment. However, many are based either on predefined production or capacity developments11 described cost reductions related to aircraft production in a mathematical unit cost model. Since then, global cumulative production volume or overall installed capacity is used to quantify experience, attaining a good match with reality in many different technologies. However, experience curves are often neglected in energy system models, since they result in non-linear, non-convex optimisation problems which adds complexity. Modelling the endogenous cost curves leads to a better representation of the dynamics of new technologies12, but requires a significantly higher computational effort. This is especially important when modelling with perfect foresight over a large time horizon. If the cost and efficiency improvements are given exogenously to the model, the model can ‘wait’ with investments until they are profitable, while in reality, costs would only dynamically decrease as investments take place. Nevertheless, in many models, technology trends including cost reduction or efficiency improvement, are only considered as exogenously assumptions. An example of how these exogenous assumptions overestimate future investment costs is solar photovoltaic (PV). The investment costs of solar have decreased rapidly due to successful policy support. A comparison by Krey et al.13 of the cost assumptions in 15 Integrated Assessment Models (IAM) shows that the cost of PV in 2020 have already fallen below the model expectations for 2050. Way et al. 8 show that the progressive cost projections for solar, onshore wind, batteries and polymer electrolyte membrane (PEM) electrolysis from several IAMs and the International Energy Agency (IEA) are high compared to historical developments or even above costs in 2020. Several other studies17 criticise that the link between cost reduction and capacity installation is not well represented in models and that exogenously-set constraints such as floor costs or excessively low annual growth rates lead to an underestimation of cost reductions. This highlights the need to model investment costs endogenously without assuming unduly elevated floor costs, overly limiting constraints on maximum annual expansion rates or maximum penetration of renewable energies.The concept of the experience curve, which means that costs and efficiencies improve as production increases, is not a new idea. Already in 1936, Wright21 which consider learning in multiple sectors and global developments. But because of the low temporal resolution in these models, they cannot represent the challenges of an energy system with a high share of variable renewable generation. In addition, most IAMs apply the Hotelling rule22 to determine the CO2 prices, which with endogenous learning is not always applicable23. Bottom-up techno-economical Energy System Models (ESM) can better capture the temporal variability of the energy system. However, studies applying endogenous learning only deal with the power sector28 or focus on a single country29.Endogenous cost reductions are currently used in some IAMs30 with full sector coupling and enough temporal resolution to capture renewable variability. The period between 2020-2050 is investigated with seven investment periods and perfect foresight over the whole modelling horizon. We do not specify the maximum annual expansion rates of renewable capacities nor CO2 emission targets for every single year. These additional conditions often lead to a lower computational effort but also predetermine the transition paths. In this way, we determine the cost-optimal annual expansion rates without making any assumptions about expansion limits. Such limits have been estimated to be artificially low in many studies compared to actual capacity developments. We want to address the following two research questions: What are the possible cost developments of green hydrogen production in Europe under the assumption of different CO2 budgets without fixed capacity deployment projections? How do different methods of modelling cost reduction influence the results?In this work, we explore how learning-by-doing on the full hydrogen production chain interacts with a fully sector-coupled energy model. We apply endogenous learning for electrolysis and renewable energy in the European model PyPSA-Eur-SecWe consider three different competing options for producing hydrogen: (i) grey hydrogen (via steam methane reforming (SMR)), (ii) blue hydrogen , and (iii) green hydrogen (via electrolysis). Hydrogen can be used for methanation, for heating (hydrogen boilers), electricity (fuel cells and retrofitted open cyclic gas turbines (OCGT)), in the industry, and in the transport sector. The synthetic gas from methanation can be used in the heating sector (gas boilers or combined heat and power plants (CHPs)), for industry processes or in the power sector (OCGTs or closed cyclic gas turbines CCGTs). The demand pathway for hydrogen in parts of industry and transport is exogenously defined, while in all others sectors, hydrogen competes with other ways of supplying demand. This means both demand for hydrogen (e.g. where it competes with heat pumps in the heating sector) and the supply side (e.g. if the hydrogen is produced via electrolysis or SMR with or without carbon capture), are part of the optimisation. OCGT and gas boilers for heating can be retrofitted to run flexibly with natural gas or hydrogen see Fig. .Fig. 1Ov31 based on current projects to be 2% of the investment costs. The cost of replacing the stack is not included in the fixed operational and maintenance cost (FOM) since it is assumed that the stack does not need to be replaced within the technical lifetime. The investment costs do not include costs for water purification, transformer costs, or connection fees to the transmission system. AEC is currently the dominant technology, but there are other types of electrolysis, such as PEM or solid oxide electrolysis cell (SOEC), which may play a more prominent role in the future. We analyse the impact of higher initial investment costs (comparable to the investment cost of PEM) in the There are various technologies for hydrogen electrolysis. In this study, cost and efficiency assumptions of alkaline electrolysis cells (AEC) are used since they are currently the most common electrolysers available on the market. We only consider large plants (above 100 MW) to avoid the scaling effects of very small plants. These costs consist of the equipment and installation costs. They include the expenses for the stack, power electronics, gas conditioning, balance of the plant and labour. The annual operational and maintenance costs are estimated in ref. 2 budgets. The investment costs of renewable generation capacity  and hydrogen electrolysis are endogenous and thus a result of the optimisation in the form of a piecewise-linearised one-factor experience curve. This results in a mixed integer linear problem MILP which is further described in the Methods Section. Endogenous global learning of the renewable generation capacities for solar PV, onshore and offshore wind is applied. Global learning assumes that global capacity grows proportionally to European capacity. The relative factor corresponds to today’s share. For example, if 1 GW of solar PV is newly built in Europe and the share of European solar PV capacity is 22%, the global capacity grows by about 4.5 GW. Further details about the initial investment cost assumptions of renewable generation are given in the We minimise total system costs for the period 2020-2050 with perfect foresight and investments in new capacity in a five-years interval for three different CO2 budgets and analyse the impact of various cost reduction modelling methods. Here, we show that hydrogen production costs drop to as low as 1.26 €/kgIn this study, we investigate the potential cost developments of green hydrogen production in Europe under different COoC budget, the direct total annualised system costs (ignoring any costs of climate change damages) are up to 27% higher than the +2.0oC budget  existing assets with high CO2 emissions are phased out before the end of their lifetime, (ii) large-scale investments are made before the costs are reduced by learning, and (iii) major parts of the oil demand are already supplied by synthetic fuels in 2030, which are more expensive to produce. However, total annualised system costs of the scenarios in 2050 are similar and vary only by 2% between the +1.5oC and +2.0oC budget since the investment costs decline. The annualised system costs of the +1.7oC scenario in 2050 are 2% lower compared to the +2.0oC scenarios. The reason is that investments in low-carbon infrastructure with the +1.7oC budget happen earlier, while for the +2.0oC scenarios a major infrastructure transformation with associated higher costs is needed in 2050 to meet the condition of climate neutrality. The European Union target of 55% greenhouse gas reduction in 2030 compared to 199032, applied to CO2, is within the +1.7oC and +2.0oC scenarios  for +1.5oC and +2oC respectively , the electrolysis investment costs range between 317 and 360 €/kWoC scenario sees the cost-optimal deployment of 435 GW of electrolysis which produce 36 million tonnes of hydrogen in 2030. This is clearly not realistic given the necessary scale-up of production facilities that would be required. In the scenario corresponding to a temperature increase of +1.7oC, 60 GW of electrolysis are installed by 2030 which produce 4 million tonnes of hydrogen. Under the +2oC scenario, 4 GW of electrolysis are deployed and 0.1 million tonnes of hydrogen are produced . A large sequestration potential of 2000 MtH2) and capture rate (90%) leads to production of blue hydrogen with a share of 19% of total production. With more optimistic assumptions on capture rate (100%) and CO2 storage potential (2000 MtH2.The production of hydrogen switches from SMR (grey hydrogen) to electrolysis (green hydrogen) in all scenarios, while SMR in combination with carbon capture (blue hydrogen) is not installed in any scenario. To further explore the option of SMR with carbon capture, we run sensitivity scenarios for blue hydrogen production depending on capture rate, investment costs and available COoC budget, green hydrogen is already produced in 2025, while in the scenario with a +2oC budget hydrogen is supplied by SMR until 2040–2045  or 2045 (+2.0oC). The REPowerEU plan6, with targeted PV capacities of 750 GWDC37 (which corresponds to 600 GWAC) by 2030, lies within our results of +1.7oC with 764 GW and +2oC with 422 GW. However, the wind expansion targets of REPowerEU with 480 GW38 by 2030, lag behind our findings with at least 555 GW in the +2oC scenario by 2030.In order to achieve net-zero emissions in 2050, renewable generation capacity must be strongly expanded in all scenarios to at least 3.2 TW solar, 1.7 TW onshore wind, and 175 GW offshore wind. The timing of the capacity build-out differs across the individual scenarios: with an ambitious budget, there is a strong expansion between 2030–2040, while in the other scenarios the strongest expansion takes place in later years from 2040  for renewable generation capacity in 2050 range between 171–237 €/kW for solar PV, 818–900 €/kW for onshore wind, and 1327 €/kW for offshore wind from the tight +1.5oC budget are significantly higher than the historical record, which emphasises the challenge to stay within this budget. For example, the average annual build out rate is 77 GW for solar PV in the +1.5oC scenario between 2020–2030. This corresponds to almost a tripling of the historical maximum annual expansion rates in Europe39. The same applies to onshore and offshore wind, with average annual build-out rates of 97 GW and 16 GW between 2020–2030 in our scenario, which are roughly five times the historical maximum annual build-out rates41. Between 2030–2040 even higher build rates are required of up to 200 GW solar capacity per year while the annual expansion of onshore wind decreases to 58 GW. A sensitivity analysis, in which the maximum annual expansion rates of renewables are limited, can be found in the oC scenarios more achievable.The build-out rates of renewables and electrolysis in scenarios with a +1.52 emissions are assumed in order to investigate what a cost-optimal system without a carbon target looks like. As in the previous scenarios, the investment costs of renewables and green hydrogen are subject to endogenous experience curves. Compared to the current system, the share of renewable hydrogen increases even without climate targets. CO2 emissions reduce from historical levels of 3.2 Gt/a in 2020 to 1.9 Gt/a in 2050  the endogenous method where investment costs are adjusted according to the installed capacity, (ii) the standard exogenous method with given fixed cost trajectories for each technology and investment year and (iii) the sequential method. In the sequential method, the optimisation problem is first solved using the exogenous cost assumptions, then the investment costs are updated depending on the optimised installed capacities. The same experience curves are assumed as in the endogenous method. The process of solving and updating investment costs is iteratively repeated until the difference of investment costs between two iterations is below a threshold. The threshold is set to a maximal mean square difference between optimised investment costs of the current and the previous iteration of 5%. The sequential method is a linear problem that requires less computational resources than the MILP of the endogenous method, but unlike the exogenous method, the investment costs are adjusted based on the installed capacities.oC budget, the sequential and exogenous methods result in up to 7% and 13% higher annualised total system costs compared to the endogenous method. The cost difference between the +1.5oC and the +2.0oC budget is smaller with the endogenous method compared to the sequential and exogenous method, because although larger capacities of renewables and electrolysis are needed at an earlier point in time, the costs also decrease more due to the faster scaling up and the foresight of the endogenous method of potential investment cost reductions. The endogenous method, therefore, allows a better comparison of costs of scenarios with different infrastructure needs or transition speeds.The cost difference of not using endogenous learning-by-doing is shown in Fig. oC scenarios in 2025, 214 GW of electrolysis are installed in the endogenous scenarios and only 20 GW electrolysis in both the sequential and exogenous cost scenarios. With the endogenous method, the hydrogen is used for the synthesis of fuels and methane earlier and to a larger extent. In scenarios corresponding to a +1.7oC budget about 1800 TWhThe endogenous method leads to an earlier deployment of the learning technologies since it is the only one of the three methods that has the foresight of how far costs can decrease. As a result, investments are made early in order to reduce investment costs. With the sequential and exogenous methods, investment is delayed and the model ‘waits’ until costs fall. For example in +1.5oC budget hydrogen costs drop to 1.32 €/kgThe prices for hydrogen are an output of the linear optimisation and are determined by the dual variables. For the exogenous and sequential method, these are obtained directly from the optimisation. In the endogenous scenarios, the investment costs and capacities of the learning technologies determined from the optimisation are assumed fixed and the optimisation is rerun as a linear problem. The exogenous method overestimates the cost of hydrogen by up to 67% in 2030 and 38% in 2050 compared to the endogenous scenarios. For example, in endogenous scenarios with a +1.52 budget and not by the modelling method , which are below the sequential optimised investment costs of 79 €/kWelec and the exogenous assumptions of 250 €/kWelec. The produced volume of hydrogen differs between the methods. For example, in scenarios corresponding to a +1.5oC budget, 24% and 30% less hydrogen is produced with the sequential and exogenous methods in 2030. With the endogenous method, more hydrogen is used for methanation and for re-electrification in fuel cells compared to the other two methods.The system composition in 2050 is primarily influenced by the assumed COTechnology learning depends on global developments while most ESM model single regions or continents. Cost in Europe, for example for solar PV, would reduce if solar panels are employed at a large scale in China. In this study, we have assumed that global renewable capacities increase in proportion to the growth in Europe. For electrolysis, we assume local learning. The exogenous method can provide a better description of cost developments for technologies for which large expansion rates outside the modelled region are expected. One could circumvent this problem with the sequential and endogenous method by splitting up the technology learning into two factors describing regional and global learning. The regional factor depends on the installed capacities in the regional model, while the global factor describes an exogenous cost decrease dependent on expected global development. The split into two factors was outside the scope of this study.42 with 12 threads, the scenarios with endogenous learning need about 21 hours to solve and require 30 GB RAM, while the sequential models solve in less than 1 hour with only 3 GB RAM and the exogenous method solves in 1 minute with only 3 GB RAM. The sequential and the exogenous method require lower computational effort and thus offer the possibility to calculate e.g. with higher spatial resolution. The solution time and memory requirements for the endogenous method increase with the number of modelled learning technologies. In contrast, the computational effort of the sequential method is independent of the number of learning technologies, since the costs are only updated after optimisation. This allows us to consider cost reductions for all technologies depending on the installed capacity without increasing the computing time.The exogenous and sequential method require significantly less memory and computing time compared to the endogenous method. For example, using the commercial solver GurobiThe chosen method of modelling technology learning should depend on the particular research question. The sequential and exogenous method are advantageous if the available computational resources are small or a greater level of detail  is important. The number of technologies that are subject to learning can be increased with the sequential method without additional computational effort. The exogenous method can represent developments outside the modelled region. If the cost reductions are expected primarily through local learning within the modelled region, the sequential and endogenous methods are appropriate. The endogenous method is favourable if the timing of the investment is analysed, costs of different climate target scenarios are compared or trade-offs between emerging technologies are considered. Technologies with a large learning potential can be better modelled with the endogenous method, since small additional capacities already lead to strong cost reductions.43, Hydrogen council of 1.4 €/kg44 and BloombergNEF of 0.68-1.55 €/kg45. In contrast to our study, these studies assume an average electricity price and a fixed number of full load hours for electrolysis and thus cannot reflect the system advantage of electrolysis running at very low electricity prices. However, we only assume local learning for electrolysis and do not consider learning due to capacity expansion in other regions, while the other studies analyse global developments. Odenweller et al.46 show that fast scale-ups of electrolysis capacities until 2030 as we see in our +1.5oC scenarios may be infeasible. However, in this study, we want to show the cost-optimal capacities that are necessary to achieve a given CO2 budget. The demonstrated findings have multiple limitations, firstly in the approach used to model experience curves and secondly in the overall assumptions made for the scenarios. For example, we make the simplified assumption that the electrolysis costs are only influenced by local learning. However, in case electrolysis is scaled up in China or the US, this would also lower the costs in Europe. Furthermore, we assume no imports of hydrogen, which would reduce the need for renewable capacity and electrolysis in Europe.In the following, we compare our costs for green hydrogen production with other studies and outline the limitations of this work. In the 2 budgets. In all scenarios, CO2 neutrality is required as an additional condition in the model by 2050. In the second part, we explore the trade-offs of three different methods modelling learning-by-doing.In this study, we use a sector-coupled European model with endogenous cost reductions through experience curves for electrolysis and renewable generation technologies, assuming different COoC warming require a rapid transformation of the energy system already in 2025 and high build-out rates of both electrolysis and renewable generation. This indicates that, without negative emissions after 2050 or further efforts such as sufficiency measures, the scenarios with +1.5oC warming are difficult to achieve. Hydrogen production shifts from grey to green hydrogen. Depending on climate targets, more than half of hydrogen demand is met by electrolysis in 2025 (+1.5oC scenario) or 2045 (+2.0oC scenario). The option of blue hydrogen is not used in any scenario.We find that in scenarios with ambitious climate targets, costs for green hydrogen electrolysis can be reduced to 1.26 €/kgoC target. While for the former, the European Union’s targets for electrolysis are in line with our +1.5–1.7oC budget scenarios, for the latter, the proposed capacities for wind and solar in REPowerEU6 are behind the capacities necessary to provide sufficient green electricity.A rapid build-up of both electrolysis and renewable generation capacity is necessary by 2030 to stay within a +1.5–2We show that ignoring the virtuous circle between capacity expansion and lower costs leads to delayed investments. A comparison of total costs of scenarios with different transformation speeds should consider cost reductions depending on the usage of technology. A faster expansion of technology than predicted in the exogenous cost assumptions thus leads to lower costs, a slower expansion to higher costs. In our results, total annual system costs are thereby up to 13% higher and levelised cost of hydrogen increase by up to 67% with the exogenous compared to the endogenous method. A middle ground approach where costs are updated sequentially offers the advantage of a lower computational effort compared to the endogenous method and maintains the correlation between investment costs and capacities.Significant cost reductions in the production of green hydrogen to 1.26 €/kg30, which minimises total system costs while optimising generation, storage and distribution capacity and dispatch. It covers energy and feedstock demand in the sectors electricity, heating, transport and industry. The model has already been presented in detail in various publications49, so in the following only the newly implemented features for this study are presented.We use the open-source European sector coupled model PyPSA-Eur-Sec2 budgets of 25.7, 45 and 73.9 Gt CO2 are assumed for the whole modelling horizon. These budgets correspond respectively to warming of +1.5oC, +1.7oC, +2oC, assuming a per capita share of the global CO2 budgets (further explanations about the chosen budgets are given in an earlier publication33). The CO2 emission paths are not fixed, except that CO2 neutrality (or negative emissions) is enforced for 2050, in line with the European Commission’s target for net-zero greenhouse gas emissions.The period from 2020 to 2050 is modelled, with perfect foresight and 7 investment periods at 5-year intervals. Three different CO9 and the open-source package powerplantmatching50. Costs, lifetime and efficiencies are assumed for the respective year of the Danish Energy Agency DEA31. The investment costs of renewable generation capacity  and hydrogen electrolysis are in the endogenous case not exogenously specified but are part of the optimisation in form of a piecewise-realised one-factor experience curve. This results in a mixed integer linear problem MILP which is further described below. The total system costs are not discounted by a social discount rate that reflects the value of future investments in order to investigate the impact of learning in isolation from other effects. A high discount rate leads to a significantly lower weighting of costs in 2050 and thus shifts investments into the future while endogenous learning leads to earlier investments.Existing generation capacities  are taken from the IRENA 2020 reportThere are three different competing options for producing hydrogen in the model: (i) grey hydrogen (via steam methane reforming (SMR)), (ii) blue hydrogen (SMR + carbon capture) and (iii) green hydrogen (via electrolysis). Hydrogen can be used for methanation, for heating (hydrogen boilers), electricity (fuel cells and retrofitted OCGT), in the industry, and in the transport sector. The demand pathway for hydrogen in parts of industry and transport is exogenously defined, while in all others sectors, hydrogen competes with other ways of supplying demand in these sectors. This means both demand for hydrogen (e.g. where it competes with heat pumps in the heating sector) and the supply side, for example if the hydrogen is produced via electrolysis or SMR, are part of the optimisation. OCGT and gas boilers for heating can be retrofitted to run flexibly with natural gas or hydrogen Fig. . There a2 emission paths are specified. Those constraints often reduce strongly the solution time of the optimisation problem, but also predetermine the transition paths. Since we consider multiple sectors and investment periods, the optimisation problem is aggregated spatially and temporally to make it computationally solvable. Spatially, energy transmission networks are reduced to a single node for Europe, while six different typical regions are used to represent the variability of renewable generation. We optimise the power transfer capacity between transmission and distribution level. No existing grid infrastructure of distribution grids is assumed. Losses in distribution are neglected. Costs of the distribution grid of 500 €/kWelec are applied. Electricity demands, heat pumps, resistive heaters, rooftop PV, home batteries, and electric vehicles are connected to the distribution grid. All remaining technologies of the power sector  are connected to the high-voltage grid. In the 51 or Heuberger et al.28 using 11 temporal days. The 10 typical days are obtained through k-medoids clustering using the Python package tsam53, so that they represent the average statistics of weather and demand, while also capturing more extreme events. To find the optimal solution we use the commercial solver Gurobi42 using 12 threads.In contrast to other studies, no maximum annual expansion rate of renewable generation capacity and no annual COc decrease by a constant factor α with each doubling of experience E55. In this study, the global cumulative capacity is used as a proxy for experience. c represents the investment costs [EUR per MW], c0 the initial investment costs [EUR per MW] Tables Experience curves are an economic concept based on empirical evidence in which the specific investment costs entclass1pt{minimaentclass1pt{minima25 to integrate experience curves within ESM: direct non-linear implementation and piecewise linear approximation of cumulative costs. In this paper, we follow the latter and use special ordered sets of type 2 (SOS2). Compared to the non-linear implementation this has several advantages: it can find a global minimum rather than getting stuck in a local one, it does not depend on the initial starting point of the solver, and it can be solved faster using commercial solver algorithms.Experience curves make ESM optimisation problems both non-linear and non-convex, which makes solving particularly challenging. There are two main approachesα ≠ 1 → LR ≠ 0.5 this results inThe cumulative investment costs for technology can be obtained by integrating the experience curve Equation . For α ≠nts Fig. . The gre56 6, global MARKAL 6–8, MARKAL-Europe 6–2057. Heuberger et al. 28 5. In this study we assume five line segments. This corresponds to six interpolation points i ∈  where N is the number of interpolation points.Other models use the following number of segments: In ERIS27: line segments at the beginning of the learning are shorter to capture the steep part of the experience curve more precisely. With each line segment the cumulative cost increase doubles.The definition of the line segments follows Barreto’s approachδs,t,i ∈  for each technology s (e.g. solar PV), investment period t and interpolation point i ∈  of the linearisation. N is the total number of interpolation points used for the piece-wise linearisation. The continuous variable indicates which line segment is active. Only two adjacent delta variables are non-zero at the same time t for technology s and their sum is equal onei is active then only δs,t,i and δs,t,i+1 are non-zero.We define a set of continuous variables Es,t of a technology s, time t and interpolation points i is defined as a summation of the product of the continuous variable δ and the x-position of the interpolation points i is active, then (4) will interpolate between The cumulative capacity s,t per investment period in Europe is the difference of the cumulative experience weighted by a global factor gfThe new installed capacity capE with the help of the SOS2 variables δ and the y-position of the interpolation points If no time-delay for the learning effects would be considered, one could express the cumulative cost TC similar to the cumulative experience t depends on the cumulative installed capacities at the previous investment period t − 1. This represents learning effects more realistically, as investment costs do not decrease immediately in the same reference year as the emerging technology is employed, but are subject to a time lag. One should be aware that this results in an overestimating of the cumulative cost curve shown exemplary in Fig. ms,t−1,i is the slope of the line segment at the previous investment period t − 1. As the total costs are the integral of the experience curve, the slope ms,t,i is equivalent to the specific investment costs.In this study we consider a temporal-delayed learning effect which means that the investment cost decrease in an investment period s,t are defined asThe overall investment costs per investment period invSupplementary InformationPeer Review File