key: cord-0982789-mnod3b1y authors: Bienstock, S. title: A flexible COVID-19 model to assess mitigation, reopening, virus mutation and other changes date: 2020-07-11 journal: nan DOI: 10.1101/2020.07.09.20150029 sha: 9da50ca067b8c0dfdd49733683748a40f0419598 doc_id: 982789 cord_uid: mnod3b1y The COVID-19 epidemic which began in China last year has expanded worldwide. A flexible SEIRD epidemiological model with time-dependent parameters is applied to modeling the pandemic. The value of the effective reproduction ratio is varied to quantify the impact of quarantines and social distancing on the number of infections and deaths, on their daily changes. and on the maxima in these daily rates expected during the epidemic. The effect of changing Reff is substantial. It ought to inform policy decisions around resource allocation, mitigation strategies and their duration, and economic tradeoffs. The model can also calculate the impact of changes in infectiousness or morbidity as the virus mutates, or the expected effects of a new therapy or vaccine assumed to arrive at a future date. The paper concludes with a discussion of a potential endemic end of COVID-19, which might involve times of about 100 years. The epidemic of novel coronavirus disease 19 has expanded rapidly to over 220 countries and all U.S. states, and upended the lives and 20 livelihoods of much of the world's population. Over ten million cases and more than 500,000 21 deaths have been reported worldwide, of which 2.7 million and 128,000 respectively in the 22 . CC-BY-NC 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 (which was not certified by peer review) United States as of July 1, 2020 (1) . The pandemic and associated community mitigation 23 measures, have had a large negative economic impact as well. The virus could trim global 24 economic growth by 3.0% to 6.0% in 2020, with a partial recovery expected in 2021 (2). 25 Unemployment in the United States temporarily surged to levels not seen since the 1930s. Here I outline a differential equation-based SEIRD model with time-varying parameters 41 and apply it to COVID-19 epidemic data. I discuss some of the potential implications of 42 community mitigation strategies and their weakening in order to reopen the economy. This 43 modeling approach is able to follow the entire development of an epidemic, from inception to 44 eradication or endemic equilibrium, if desired. The model helps quantify tradeoffs in terms of 45 . CC-BY-NC 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 July 11, 2020 . . https://doi.org/10.1101 /2020 additional cases and deaths in a given region and their maximum rates of increase, expected to 46 result from a weakening of social distancing, or "reopening". It can also be used to assess the 47 impact of changes in a pathogen's infectiousness or morbidity over time. Model and parameters 49 SIR and SEIR compartmental epidemiological models have been studied for nearly one 50 hundred years. The term "compartmental" may have originated by analogy to trains or ships, 51 essential modes of transportation in the first part of the twentieth century. In the non-autonomous 52 SEIRD model discussed here, a population is divided into five non-overlapping classes, known 53 as compartments: 54 • S, susceptible hosts; 55 • E, exposed hosts, presumed to be latently infected but not yet infectious; 56 • I, infectious hosts; 57 • R, hosts recovered from the exposed and infectious population and, rate from Susceptible to Exposed is calculated. Other required data are the transition rates from 65 each group to the next. An E host can either get infectious (move to I) or recover (move to R), 66 and an I host can either move to R (recover) or move to D (die from the disease). All Recovered 67 hosts are assumed to be immune, or "removed" from the epidemic, although it is possible to 68 . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint relax this assumption. Hosts in all groups but D can also die for reasons unrelated to the 69 infection, at an average rate. Finally, a gross birth rate for the Susceptible group is specified, and This provides a check on the accuracy of the numerical solution. All calculations were performed 78 in the R Statistical Environment (5). The differential equations were easily integrated out to 100 79 years using the ode function in R (6) (7) (8) in order to explore the long-term behavior of the 80 solutions. For practical uses, the focus is on the first year or two. A rapidly growing set of reports on the COVID-19 infection parameters is becoming 82 available online. Table 1 lists those used in this study (9) (10) (11) (12) (13) (14) (15) The model allows the study of an epidemic from beginning to end. All of the model 85 parameters can vary with time to reflect, for example, a change in social distancing, a mutation 86 that alters the pathogen's infectiousness, or a reduction in morbidity expected from a new 87 therapy available as of some point in the future. Coupled with a modern differential equation 88 solver (8), the model generates accurate results in seconds, which makes it feasible to perform 89 sensitivity analyses with respect to one or more of the parameters used, as shown below in 90 . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint per day. As can be seen from Figure 3 and Table 2 , the effect of a change in Reff on these 113 maximum daily rates is quite large. This type of information could be used to assess whether a 114 . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint relatively early weakening of quarantine and social distancing in a given region, leading to a 115 substantial increase in Reff, would result in an acceptable number of additional casualties. [ Table 2 CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020 . . https://doi.org/10.1101 /2020 Discussion 138 A SEIRD epidemiological model with time-dependent parameters was presented, able to 139 follow an epidemic from inception to eradication or endemic equilibrium, and applied to 140 COVID-19 data. By varying the value of the pathogen's effective reproduction ratio, the model CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. ϕ . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020 . . https://doi.org/10.1101 /2020 R₀ has the following interpretation: it is the product of the production rates of E and I per unit CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020 . . https://doi.org/10.1101 /2020 . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint . CC-BY-NC 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. The copyright holder for this preprint this version posted July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint . CC-BY-NC 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 July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint CC-BY-NC 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 July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint . CC-BY-NC 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 July 11, 2020. . https://doi.org/10.1101/2020.07.09.20150029 doi: medRxiv preprint COVID-19 situation update worldwide Global Economic Effects of COVID-19 World Bank. Updated estimates of the impact of COVID-19 on global poverty 19-global-poverty 188 4. CDC and ESPR. COVID-19 Pandemic Planning Scenarios R: A language and environment for statistical computing Foundation for Statistical Computing Solving Differential Equations in R. 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