In the Indian subcontinent, about 200 million people are at risk of developing visceral leishmaniasis (VL). In 2005, the governments of India, Nepal and Bangladesh started the first regional VL elimination program with the aim to reduce the annual incidence to less than 1 per 10,000 by 2015. A mathematical model was developed to support this elimination program with basic quantifications of transmission, disease and intervention parameters. This model was used to predict the effects of different intervention strategies. Parameters on the natural history of Leishmania infection were estimated based on a literature review and expert opinion or drawn from a community intervention trial (the KALANET project). The transmission dynamic of Leishmania donovani is rather slow, mainly due to its long incubation period and the potentially long persistence of parasites in infected humans. Cellular immunity as measured by the Leishmanin skin test (LST) lasts on average for roughly one year, and re-infection occurs in intervals of about two years, with variation not specified. The model suggests that transmission of L. donovani is predominantly maintained by asymptomatically infected hosts. Only patients with symptomatic disease were eligible for treatment; thus, in contrast to vector control, the treatment of cases had almost no effect on the overall intensity of transmission. Treatment of Kala-azar is necessary on the level of the individual patient but may have little effect on transmission of parasites. In contrast, vector control or exposure prophylaxis has the potential to efficiently reduce transmission of parasites. Based on these findings, control of VL should pay more attention to vector-related interventions. Cases of PKDL may appear after years and may initiate a new outbreak of disease; interventions should therefore be long enough, combined with an active case detection and include effective treatment.
VL, also called Kala-azar (KA), causes more than 50,000 deaths each year worldwide [5]. The name ‘Kala-azar’ (‘black-fever’) originates from India; it refers to the hyperpigmentation of the skin during the course of the disease. In contrast to CL and MCL, where the parasites are localised in tegumentary tissue, VL is a systemic infection of the phagocytic and reticulo-endothelial system; this infection includes the lymph nodes, spleen and liver. Clinical symptoms of VL are prolonged fever, fatigue, weight loss, bleeding tendency and an enlarged spleen and liver. Pancytopenia is also a characteristic sign. PKDL, first described by Brahmachari in 1922 [6], can occur as a sequel to KA. It usually develops 6 months to several years after treatment and putative recovery from KA [7]. Poor treatment compliance is thought to favour the occurrence of PKDL [8], but a small fraction of PKDL cases have no reported history of KA [9]. The nodular lesions of PKDL patients usually contain many parasites [10]. PKDL is not a life-threatening condition, laboratory confirmation is challenging, and the treatment burdens the patients (in Bangladesh, current treatment guidelines call for 120 intramuscular injections of sodium stibogluconate [9]). Therefore, it is assumed that many patients remain undiagnosed and untreated, and PKDL patients are thought to act as a reservoir of infection [11]. Cases with VL and HIV co-infection have been reported from 35 countries. Both cellular and humoral responses to Leishmania are diminished in such patients [12], leading to an increased risk of developing VL after Leishmania infection and a higher rate of treatment failure [13], [14]. The rate of HIV-VL coinfection in the Indian subcontinent is still low but rising in Ethiopia. HIV-coinfected patients are relevant for the study of transmission, as they are more infectious due to higher parasitaemia [15]. The classical confirmatory test for VL used to be the microscopic detection of amastigote parasites from aspirates of lymph nodes, bone marrow or spleen [16]. This invasive method has largely been replaced by antibody-detection using rK39 immunochromatographic tests or by the direct agglutination test (DAT) [2]. Several PCR techniques have been developed. They seem to be more sensitive for detecting asymptomatic infections than the antibody tests [17], as it is hypothesised that PCR of peripheral blood will be the first marker to become positive after infection (before antibody seroconversion takes place). The leishmanin skin test (LST) is a marker of the delayed-type hypersensitivity reaction and is used in epidemiological surveys to study what proportion of the population has become ‘immune’ to leishmanial infection after exposure. When taking a bloodmeal on an infected host, female sand flies ingest the amastigote form of the parasites. In the sand fly gut, the parasites develop into procyclic promastigote flagellar forms, which divide and later on differentiate into metacyclic promastigotes. These forms migrate to the pharyngeal valve and can then be transmitted at subsequent blood meals. In the human host, parasites change back to amastigotes and multiply in cells of the mononuclear phagocyte system, impeding the immune defence mechanisms of macrophages [18]. In 2005, the governments of India, Nepal and Bangladesh started the first regional VL elimination program, aiming to reduce the annual incidence of VL to less than 1 per 10,000 by 2015. The program focuses on treatment-related control strategies, such as early diagnosis and complete treatment, and vector-related control strategies, including indoor residual insecticide spraying. Currently, four drugs for VL treatment are available. 1) Pentavalent antimonials have been the first-line treatment for over 70 years. This treatment is long (20 to 30 days), is toxic (3–5% deaths due to treatment) and is accompanied by increasing failure rates; for instance in foci of the Bihar state, India, with up to 60% treatment failures, a phenomenon that is assumed to be caused by drug resistance [19]. 2) Miltefosine is the first oral drug against VL and has been recommended as first-line drug in the VL elimination initiative but is teratogenic and is suspected to rapidly give rise to resistance due to its long half-life. 3) Amphotericin B is used in two formulations: “Conventional” Amphotericin B and “Liposomal” Amphotericin B (Ambisome). Treatment with the conventional formulation is long (30 days) and can have life-threatening side effects whereas treatment with the liposomal formulation is shorter, has similar high efficacy and fewer side effects; Yet it is too expensive and complex in its administration for large-scale application in developing countries. However recently, a single-dose Ambisome schedule was found highly effective in India [20]. 4) Paromomycin (PMM) was registered in 2006 in India and is currently being tested in a phase IV trial [2], [21]. The first mathematical study of the dynamics of KA employed a deterministic model to explain the observed inter-epidemic periods between 1875 and 1950 in Assam, India [25]. This model was later extended to canine visceral leishmaniasis in Malta, considering three different serological tests for the presence of specific antibody in dogs [26], [27]. In a further extension, the efficacies of various control methods, such as vaccination, killing infected dogs, drugs and insecticides, were investigated by means of sensitivity analyses [28]. A recent modelling paper addressed the question of under-reporting of VL in Bihar, India. [29]. Our model focuses on the transmission dynamics of L. donovani in the Indian subcontinent and extends the before-mentioned modelling findings with (i) quantifications of epidemiological parameters for the natural history of infection and transmission dynamics of L. donovani and (ii) databased predictions for the effects of different intervention strategies; in particular, the roles of asymptomatic and symptomatic infections are considered.
The transmission dynamics of L. donovani in the Indian subcontinent was modelled deterministically by a system of ordinary differential equations. Figure 1 describes the model graphically, and Table 1,2 and 3 provide lists of parameters and variables with references. In this section, we describe the basic structure of the model; the full model, considering also possible animal hosts and immuno-compromised humans, is provided in Text S1 with Figure S1 showing the full model. The basic Susceptible-Infected-Recovered (SIR) type model was modified with respect to the history of infection, considering five stages in the natural history of infection. These stages were described based on different combinations of three diagnostic markers to categorise people living in endemic areas: PCR (index P, earliest marker for L. donovani infection), DAT (index D, antibody response) and LST (index C, suggesting a state of ‘cellular’ immunity). Superscripts “+” and “−” represent positive and negative results, respectively. If the infection proceeded asymptomatically, we assumed that the human host (indicated by subscript H) typically passed through the following five stages: SH: Susceptible stage (P−D−C−). Hosts are negative for all three markers and can become infected in the future. IHP: Early asymptomatic, infectious stage (P+D−C−). The parasite can be detected by PCR, but there is not yet any humoral or cellular response in the host. IHD: Late asymptomatic, infectious stage (P+D+C−). Hosts are still PCR-positive and antibodies can be detected by DAT. RHD: Early recovered stage (P−D+C−). The parasite cannot be detected anymore, but hosts are DAT-positive and not yet LST-positive. RHC: Late recovered stage (P−D−C+). Hosts are DAT-negative but still LST-positive and assumed to be protected against re-infection. Model solutions were numerically computed using the software Matlab Version 7. 120635 (R2011a) by a Runge-Kutta algorithm with variable step size (procedure ode15s). Parameters were estimated by fitting the model to observations from the KalaNet project (DAT- and PCR-positivity, symptomatic VL and sand fly infection) and information from the literature (LST-positivity, prevalence of HIV and prevalence of HIV-infected among symptomatic VL). We used the model to estimate the following eight parameters: The parameter vector was estimated by Maximum Likelihood with likelihood functionwhere by exponents k1 to k22 represent sample sizes observed in the KalaNet trial or taken from the literature (for references see Table 1,2, 3 and Table S1). These exponents are partially not integer values, because sample sizes for the estimation had to be back calculated considering the prevalence of HIV-positive hosts, yielding The likelihood was maximized by minimizing the negative log-Likelihood −ln (L), using Matlab procedure fminsearch. Confidence intervals were computed by the profile likelihood [34], i. e. the parameter of interest was minimised (lower confidence limit) or maximised (upper confidence limit) conditional on that the likelihood worsens only according to χ2/2 with 1 degree of freedom, i. e. 3. 84/2, whereby the other 7 parameters may vary as nuisance parameters. Parameter values, estimates and confidence intervals are shown in Tables 1,2, 3 and Table S1.
The parameter estimates (Table 1, Table 2, Table 3 and Table S1) originate from fitting the model to data of which prevalences have been estimated as described in the Methods section were as follows 26% of the human population (SH) were negative for all three markers of PCR, DAT and LST (P−D−C−), 10% (IHP) were PCR-positive (P+D−C−), 2% (IHD+IHS+IHT1+IHT2+IHL) were PCR- and DAT-positive (P+D+C−), 12% (RHD+RHT+RHL) were DAT-positive (P−D+C−) and 50% (RHC) were LST-positive (P−D−C+). Model-based rates and durations in the natural history of infection were estimated from the prevalences for humans as follows. Humans remained on average 1/ (λH+μH) = 150 days in the susceptible state (SH) before they became infected. After infection, PCR-positivity lasted on average for 1/ (γHP+μH) +1/ (γHD+μH) = 72 days (approx. 95% CI: 69 to 75 days) and overlapped with DAT-positivity, which lasts for asymptomatic individuals for 1/ (γHD+μH) +1/ (ρHD+μH) = 86 days (approx. 95% CI: 74 to 99 days). For an overlap period of about 1/ (γHD+μH) = 12 days, asymptomatic individuals were positive for both markers (late asymptomatic state IHD). This means that individuals without symptomatic disease need on average about 146 days to develop LST-positivity after a PCR-positive finding. LST-positivity lasted on average 1/ (ρHC+μH) = 300 days (approx. 95% CI: 255 to 348 days). As population turnover alone is not sufficient to yield a prevalence of 26% susceptibles (negative for all three markers: P−D−C−), loss of LST-positivity must be assumed to explain these, together with a prevalence of 50% LST-positive individuals in the population. Taken these durations together, humans with an asymptomatic course were infected on average every 596 days (= 150 days SH+60 days IHP+12 days IHD+74 days RHD+300 days RHC). As heterogeneities are not taken into account, one might crudely assume that humans become infected every one to three years. Given a 0. 5% prevalence of infected sand flies [35] and the above-mentioned prevalences, the probability pF2 that a sand fly is infected during a blood meal on an asymptomatic host (IHD) was estimated at 2. 5% with 95% CI (1. 2% to 3. 8%). This estimate is robust against changes in the infection probability for flies feeding on symptomatic hosts, which was assumed to be pF3 = pF4 = 100%. A sensitivity analysis in which pF3 and pF4 were reduced to 10% had no relevant effect on the estimate for pF2, which then decreased from 2. 5% to 2. 3%. The reason for this minor contribution of symptomatically infected hosts to the overall transmission is simple: their prevalence is too low compared to the abundance of asymptomatically infected hosts. The estimates reported so far are correlated with the time between blood meals of sand flies (assumed with 1/β = 4 days [36]) and the ratio NF∶NH of vectors to humans (estimated at 527∶100, with 95% CINF (347 to 990) ). We investigated interventions recommended by the VL elimination program, including treatment-related control strategies, such as early case detection or treatment optimisation. We also considered vector-related control strategies, such as breeding site control, indoor spraying or use of bed nets, to explore possibilities and constraints in VL control.
The transmission dynamics of L. donovani are rather slow, mainly due to the long incubation period and the potentially long persistence of parasites in infected humans. Parasite DNA can be detected in infected human hosts for two to three months; after seroconversion, antibodies can be detected for about the same period of time in those humans who do not evolve to clinical disease. These periods overlap for a few weeks only, when both parasites and antibodies are detectable in peripheral blood. Few infected humans become clinically sick. The majority of infected hosts are estimated to become LST-positive five to six months after infection, without showing any sign of disease. LST-positivity, which is assumed to represent a state of protective cellular immunity, is estimated to persist for about one year. Without loss of LST-positivity, the model would lead under realistic birth and death rates of humans to over 90% LST-positive individuals in the population. For analysing the process of human recovery, published studies involving the LST were used to estimate the duration of the cellular immune response based on LST-positivity. Previous studies reported prevalences of positive LST results among recovered KA patients (who are expected to be LST-positive) ranging from 30% to 80% [33]. These studies suggested that the lowness and variability of LST sensitivity is affected by the leishmanin antigen suspension chosen. Because an antigen based on South Asian L. donovani is not available, all LST data refer to L. infantum or L. major antigens. There is extensive cross-reactivity of patient responses to heterologous Leishmania species, but as the variable results underscore, there is a need for better standardisation and documentation of sensitivity and stability of leishmanin antigens to obtain more reliable data on the state of cellular immunity. Effects associated with differing proportions of LST-positive individuals are explored in the section on sensitivity analyses below. Apart from problems with the antigen (see above), there are in principle two possibilities to explain a proportion of only 50% LST-positive individuals (cf. before: >90% LST-positive individuals would be expected under the assumption of life-long LST-positivity). These two explanations depend on how infection spreads, as follows: 1) If infection is clustered (e. g. , within-household transmission predominates due to a low rate of transmission between households) then life-long LST-positivity may exist on the level of the individual, and a low, ‘average’ LST-prevalence in the population must result from the demographic process, i. e. , it must result from deaths of LST-positive individuals and the births of individuals who are LST-negative. 2) If infection is not clustered, but spreads homogeneously within the human population, then a low LST-prevalence in the population must involve loss of the ‘individual’ LST-positivity (as opposed to option 1 where the ‘average’ LST-positivity gets lost). As the birth rate is not sufficient to explain a prevalence of 50% LST-positive individuals (see above), we proceeded with the assumption of loss of LST-positivity. Under this assumption, humans in active L. donovani transmission foci were infected every one to three years. A considerable loss of LST positivity has been reported from an endemic VL focus in Ethiopia [37]. There, the authors concluded that the presumption of a life-long positive LST reaction may only hold true under circumstances of continued exposure to infected sand flies or subclinical infection. A short and effective treatment regimen or early case detection can reduce the prevalence of KA but has almost no effect on the incidence of the disease (Fig. 2 and Table 4). Treatment is thus an intervention that benefits the individual but not the population. The reason why treatment is not a measure to control the transmission of infection must be attributed to many asymptomatically infected hosts who are - despite a low infectivity for flies - responsible for the majority of parasite transmissions from humans to sand flies. As demonstrated by the sensitivity analysis shown in Fig. 2 and Table 4 (scenario 2), a beneficial effect of treatment on transmission cannot even be expected under over-optimistic assumptions; for instance, minimal duration of treatment and time until treatment start with maximum treatment efficacy. The KA elimination program aims for less than 1 case per 10,000. Even under over-optimistic treatment assumptions, this target would not be reached; the model suggests that elimination of VL would not succeed if intervention was based on treatment alone. The contribution of asymptomatic infections on transmission may, however, be region and strain specific, as apparent from ratios of asymptomatic infections to KA cases ranging from 6∶1 in Brazil to 50∶1 in Spain [38]. The current vector-related interventions comprise irregular indoor spraying and exposure prophylaxis, such as untreated bed nets. As summarised by [30], indoor insecticide spraying during the Indian National Malaria Eradication Program between 1958 and 1970 had a drastic impact on transmission of L. donovani. No VL cases were reported from the state of Bihar during that period. However, within months after the program was terminated, the first cases of KA re-appeared and at the end of 1970, a VL epidemic struck Bihar. In 1992, another eradication program with indoor residual DDT spraying resulted in a sharp decline from 1993 until 1999. Whereby treatment-related interventions only reduce symptomatic infection, vector control is also efficient against asymptomatic infection (Fig. 3 and Table 5). The model predicted that VL may be eliminated by reducing the vector density by 80%, which seems to provide serious options for the VL elimination program (results not shown). Prospects of successful elimination can also be expressed by the moderate basic reproduction number which this model predicts with R0 = 3. 94 (see Text S1). As found during the KalaNet study, the use of treated bed nets may not provide this efficacy. Indoor density of P. argentipes is reported in the study to be reduced by 25% in villages that used treated nets compared with control villages. This intervention reduced the annual incidence of VL at best to 18. 8 cases per 10,000, which is far from the elimination target of less than one case per 10,000. The authors hypothesised that a substantial fraction of L. donovani transmission occurring outside the house may explain the results obtained in the trial [24]. However, two other studies in the Indian subcontinent showed a much higher reduction in the sand fly density by means of vector-related interventions [22], [39]. Despite the fact that vector control has the potential to effectively reduce L. donovani transmission, it must be complemented by the treatment of KA and PKDL cases. The latter can substantially maintain a reservoir of infection, which can initiate a new outbreak of disease after vector control is stopped. As the natural history of L. donovani transmission is a rather slow process where parasites can persist in humans over a long period, interventions will show an effect after years, not months, as demonstrated in Fig. 4. PKDL cases may occur after years, and their final recovery may take months or years. If vector control is stopped before parasites are eliminated in the human hosts, then emerging PKDL cases can initiate a new outbreak of disease as soon as there are enough sand flies available for transmission. Thus, active case detection and effective short-course treatment of PKDL combined with effective vector control are required for VL elimination. To determine the role of LST-positive individuals (RHC), the default assumption of 50% LST-positive individuals was varied between 30% and 70% (76% is the maximum possible value because 24% of the human population belong to other diagnostic categories, see above). A low equilibrium prevalence of LST-positive individuals results from a lower infection rate (or lower values of correlated parameters, such as the biting rate or the number of vectors), and a high prevalence of LST-positive individuals can result from a higher infection rate (or higher values of correlated parameters, such as the biting rate or the number of vectors). The only parameter estimate that was affected within the natural history of infection by this variation of the prevalence of LST-positive individuals was the rate of loss of cellular immunity (ρHC). The estimate of 1/ρHC = 307 days of LST-positivity with the 95% confidence interval between 260 and 356 days (see Table 2) does not support the assumption of a life-long cellular immunity based on life-long LST-positivity (in technical terms, life-long LST-positivity would lead to an excessive accumulation of individuals in state RHC, which is not consistent with the data). The effects of different prevalences of infected sand flies were also analysed, as the prevalence of infected sand flies may vary regionally. The default assumption of IF = 0. 5% infected sand flies is based on data from Nepal, whereas higher prevalences have been observed in India. A higher prevalence of infected sand flies results from a lower number of flies (NF) or from a higher infection probability originating from asymptomatic hosts (pF2). We assumed that the period of DAT-positivity is the same for symptomatic and for asymptomatic cases (1/ρHD = 1/ρHT = 74 days). The estimate of ρHD (DAT-positivity in asymptomatic cases) is robust against the assumption that DAT-positivity may last longer in symptomatic cases [40]. In that investigation antibody persistence in symptomatic cases was suggested to last on average about 4 years. Such an increase, however, can be completely compensated in the model by reducing the period of DAT-positivity in asymptomatic cases from 74 to 69 days, showing that the model behaves robust against changes in these assumptions. A full factorial sensitivity analysis is provided in Fig. S2 in the Supplement. Our simulation results show that transmission of L. donovani is predominantly driven by asymptomatically infected hosts who are not eligible for treatment. Treatment can reduce the prevalence of symptomatic disease, but the incidence of KA remains on similar levels because of an unchanged intensity of transmission. In contrast to treatment-related interventions, vector-related interventions have the potential to reduce the prevalence of asymptomatic infections and thus are the intervention of choice from an epidemiological perspective. Vector control, however, should be combined with treatment, as PKDL cases can act as reservoirs of infection. This reservoir function originates from the long period of nearly two years on average during which putatively recovered KA patients develop PKDL.
Visceral Leishmaniasis is a neglected, life-threatening disease affecting the poorest of the poor. It has received more attention in light of the regional VL elimination program. A deterministic compartmental model was developed to estimate parameters for L. donovani transmission and to optimise intervention success. Our simulation results show that transmission of L. donovani is predominantly driven by asymptomatically infected hosts who are not eligible for treatment. Treatment can reduce the prevalence of symptomatic disease, but the incidence of KA remains on similar levels because of an unchanged intensity of transmission. In contrast to treatment-related interventions, vector-related interventions have the potential to reduce the prevalence of asymptomatic infections and thus are the intervention of choice from an epidemiological perspective. Vector control, however, should be combined with treatment, as PKDL cases can act as reservoirs of infection. This reservoir function originates from the long period of nearly two years on average during which putatively recovered KA patients develop PKDL.
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Visceral Leishmaniasis in the Indian Subcontinent: Modelling Epidemiology and Control