A novel COVID-19 model reveals unexpected consequences of social distancing strategies

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Jim Greene

Clarkson University
"A novel COVID-19 model reveals unexpected consequences of social distancing strategies"
Early 2020 saw the onset of the COVID-19 pandemic. As of July 14, 2020, there have been over 13 million confirmed cases worldwide, which have caused over 570K fatalities; in reality, the numbers are almost certainly much higher. As a vaccine has yet to be developed, social distancing as a form of a Nonpharmaceutical Intervention (NPI) has been enacted in many countries as a means of reducing the spread of the virus. Understanding the effects of social distancing to hopefully “flatten the curve” is fundamentally important in the design of reopening policies. In this work, we introduce a framework which explicitly models socially distanced populations via separate compartments: distancing regulations are modeled by flow rates between the distanced and non-distanced populations, and the overall reduction in transmissions due to distancing is also incorporated. In this way, both the response to distancing guidelines and their stringency can be explicitly modeled, and thus the control problem can be thought of as having two inputs from a policy-design perspective. We note that many authors have studied the control problem via reduction in transmission rate, whereas flow rate control has not been sufficiently analyzed; the latter is a focus of the current work. We compute the basic reproduction number R0, which characterizes the initial outbreak of the infection, and demonstrate that at sufficiently early stages of the pandemic when there is little immunity in the population, a quick implementation of social distancing is required in order for R0<1. We also find that R0 is sensitive to the fraction of infected individuals who become symptomatic (currently highly uncertain), illustrating the importance of obtaining a confident measurement of this value before quantitative model predictions can be trusted. Similarly, as it is currently unknown how infective asymptomatic carriers are, we investigate the dependence of R0 on distancing regulations (both flow rate and transmission reduction) as a function of the asymptomatic infection rate. Dynamic simulations of time-varying distancing guidelines also provide surprising results. We discover a critical implementation delay in issuing separation mandates. That is, there is a nontrivial but tight “window of opportunity” for commencing social distancing in order to meet the capacity of healthcare resources. Different relaxation strategies are also simulated. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule’s frequency. Furthermore, we consider the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines (which is unfortunately playing out in real-time in the U.S.), but the negative effects can be mitigated if the relaxation strategy is carefully designed.
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