Forecasting COVID-19 and Analyzing the Effect of Government Interventions

One key question in the ongoing COVID-19 pandemic is understanding the impact of government interventions, and when society can return to normal. To this end, we develop DELPHI, a novel epidemiological model that captures the effect of under-detection and government intervention. We applied DELPHI across 167 geographical areas since early April, and recorded 6% and 11% two-week out-of-sample Median Absolute Percentage Error on cases and deaths respectively. Furthermore, DELPHI successfully predicted the large-scale epidemics in many areas months before, including US, UK and Russia. Using the extracted government response, we find mass gathering restrictions and school closings on average reduced infection rates the most, at 29.9 {+/-} 6.9% and 17.3 {+/-} 6.7%, respectively. The most stringent policy, stay-at-home, on average reduced the infection rate by 74.4 {+/-} 3.7% from baseline across countries that implemented it. We also illustrate how DELPHI can be extended to provide insights on reopening societies under different policies.


Research in Context
Evidence before this study Previous research into COVID-19 has focused on reporting estimates of epidemiological parameters of COVID-19. We conducted an extensive literature search on PubMed and MedRXiv including keywords such as "non-pharmaceutical interventions" and "government interventions". We discovered some studies reporting on the theoretical e ect of non-pharmaceutical interventions in a theoretical modeling framework. ere have also been a few published studies reporting on the overall e ect of government interventions in the very early stages of the epidemics in various regions, such as the United States and Europe. However, there were few studies that tried to quantify the e ect of each policy that was implemented, and none that the authors know of that are conducted on the global scale of this paper. Added value of this study As governments continue to implement non-pharmaceutical interventions, we aim to understand the e ect of di erent policies that have been implemented in the past. We developed a novel epidemiological model that has been continuously providing high accuracy forecasts since early April. It also provides global estimates for the e ects of di erent policies as they have been implemented across 167 areas. e large number of areas we consider enable us to derive inference for many popular policies that have been implemented, including mass gathering restrictions, school closures, along with travel and work restrictions. Implications of all the available evidence e evidence indicates that mass gathering restrictions were the most e ective single policy in reducing the spread of COVID-19, followed by school closings. Stay-at-home policies greatly reduced the e ective R0 and most likely enabled the e ective control of the epidemics in many regions. Policy simulations suggest that many countries around the world are not yet suitable for a loosening of policy guidance, or there would be potentially severe humanitarian costs.
of COVID-19. DELPHI (Di erential Equations Lead to Predictions of Hospitalizations and In-16 fections) extends a classic SEIR model to include many realistic e ects that are critical in this 17 pandemic, including deaths and underdetection. Speci cally, we included an explicit nonlinear 18 multiplicative factor on the infection rate to model the spread as it happened in di erent regions. 19 Such explicit characterization of government intervention allows us to understand the e ect of 20 di erent non-pharmaceutical interventions as they have been implemented in various regions 21 while accounting for regional population characteristics including baseline infection rate and 22 mortality rate. Furthermore, we formulated DELPHI with data scarcity as a key consideration.  disease, but not con rmed due to lack of testing. Some of these people recover (U R ) and 43 some die (U D ).

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• Recovered (R): People who have recovered from the disease (and assumed to be im-50 mune).

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• Deceased (D): People who have died from the disease.

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In addition to main functional states, we introduce auxiliary states to calculate a few useful  is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 24, 2020. .

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• α is the baseline infection rate.
• γ(t) measures the e ect of government response and is de ned as: where the parameters t 0 and k capture, respectively, the timing and the strength of the 67 response. e e ective infection rate in the model is αγ(t), which is time dependent.

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• r d is the rate of detection. is equals to log 2 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 24, 2020. .
• σ is the rate of recovery of non-hospitalized patients. is equals to log 2 T σ , where T σ is the 73 median time to recovery of non-hospitalized patients ( xed at 10 days • τ is the rate of death. is captures the speed at which a dying patient dies, and thus 77 inversely proportional to how long a dying patient stays alive.

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• µ is the mortality percentage. is is the percentage of people who die from the disease 79 in a particular region. Note this quantity is independent from the rate of death.

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• p h is the (constant) percentage of detected cases hospitalized. is is set to 15%. [11,12] 82 erefore, we t on 5 parameters from the list above ( α, µ, τ, t 0 , k). In addition, we introduce two 83 additional parameters k 1 , k 2 to account for the unknown initial population in the infected (I) 84 and exposed (E) states (see Supplementary Materials for details). We thus t seven parameters 85 per area. 86 e parameters are ed by minimizing a weighted Mean Squared Error (MSE) metric with respect to the parameters. De ne DT (t) and DD(t) as the number of reported total detected cases and detected deaths, respectively, on day t. en, the loss function for a training period of T days is de ned as: where DT (t) and DD(t) are respectively the total detected cases and deaths predicted by DEL-

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PHI. e factor t gives more prominence to more recent data, as recent errors are more likely 88 to propagate into future errors. e lambda factor λ = min DT (T ) 3·DD(T ) , 10 balances the ing 89 between detected cases and deaths; this re-scaling coe cient was obtained experimentally. We 90 only include historical data starting when the area recorded more than 100 cases; this allows 91 us to exclude sporadic outbreaks that are not epidemics. In the COVID-19 crisis, one of the key modeling di culties is the chronic underdetection 98 of con rmed cases. is is both due to the lack of detection abilities in the early stages of the 99 pandemic and also the similarity between a mild case of COVID-19 and the common u. us, strong evidence. Furthermore, at the time of redaction, the serological data were largely limited to speci c sub-areas such as cities and counties (see [   6 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted June 24, 2020. .

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DELPHI was created in early April and has been continuously updated to re ect new ob-      compared to mass gathering, travel, and work restrictions is 29.9 ± 6.9%. is is further sup-199 8 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted June 24, 2020. .  Speci cally, suppose that we are considering a policy easing from policy i to j at time t c in some area. en for all times t ≥ t c , we correct the government response as follows: Di erential in policy e ect between policy i and j , ∀t ≥ t c .
Essentially, we apply a correction term that is proportional to the fractional di erence in policy  To further understand the disparate impact of the policies across countries, we made predic-231 tions for the situation around the world assuming a policy that involves mass gathering, travel, 232 and work restrictions was universally implemented on 06/16. Figure 4a shows three clusters of 233 countries for July 15th: 234 9 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138693 doi: medRxiv preprint  is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138693 doi: medRxiv preprint (a) Weekly Incidence of Cases (per 100K) in the rst half of July against fraction of population infected for multiple countries (b) Predictions for total cumulative cases (normalized by the population) vs new cases (per 100K) for countries which are predicted to be highly impacted and still worsening at an alarming rate by July 15th CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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12 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 24, 2020.