Effects of Latency on Estimates of the COVID-19 Replication Number
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Effects of Latency on Estimates of the COVID-19 Replication Number Lorenzo Sadun1 Received: 12 June 2020 / Accepted: 6 August 2020 © Society for Mathematical Biology 2020
Abstract There is continued uncertainty in how long it takes a person infected by the COVID19 virus to become infectious. In this paper, we quantify how this uncertainty affects estimates of the basic replication number R0 , and thus estimates of the fraction of the population that would become infected in the absence of effective interventions. The analysis is general, and applies to all SEIR-based models, not only those associated with COVID-19. We find that when modeling a rapidly spreading epidemic, seemingly minor differences in how latency is treated can lead to vastly different estimates of R0 . We also derive a simple formula relating the replication number to the fraction of the population that is eventually infected. This formula is robust and applies to all compartmental models whose parameters do not depend on time. Keywords Latency · SEIR · Coronavirus · Replication number · Estimation Mathematics Subject Classification 92-10 · 92B99
1 Introduction In any epidemic, there are two basic questions that need to be answered: – How much does our behavior need to change to contain and eventually suppress the outbreak? – How many people will eventually get infected if our behavior doesn’t change? Both questions boil down to estimating the basic reproduction number R0 , which describes the average number of new individuals that each infected individual goes on to infect, assuming no interventions and no depletion of the population of susceptible individuals.
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Lorenzo Sadun [email protected] Department of Mathematics, University of Texas, Austin, USA 0123456789().: V,-vol
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The connection of R0 to the first question is clear. If R0 = 1.2, then blocking 20% of would-be transmissions is enough to halt and reverse the outbreak; mild interventions, such as promoting frequent hand-washing and the wearing of masks, might be enough. If R0 = 5, then blocking 80% or more of the would-be transmissions is needed, so much more drastic actions, such as full scale lock-downs, are called for. At of July 2020, strong measures have largely halted the spread of COVID-19 in East Asia and Europe, and policy-makers there are trying to determine the extent to which these measures can be safely relaxed. In much of South Asia, Africa, and the Americas, however, where strict measures either were not imposed or were abandoned prematurely, the disease is running unchecked and policy-makers must come to grips with what measures need to be imposed or re-imposed. Throughout the world, effective public policy depends on understanding R0 . The connection of R0 to the second question is more subtle. We will see that, in a wide variety of models, the fraction x of the population that is eventually infected is purely a function of the replication number R. R, as opposed to R0 , describes the average number of new individuals that each
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