Abstract
This paper contains a theoretical study of epidemic control. It is inspired by current events but not intended to be an accurate depiction of the SARS-CoV-2 pandemic. We consider the emergence of a highly transmissible pathogen, focusing on metropolitan areas. To ensure some degree of realism, we present a conceptual model of the outbreak and early attempts to stave off the onslaught, including the use of lockdowns. Model outputs show strong qualitative—in some respects even quantitative—resemblance to the events of Spring 2020 in many cities worldwide. We then use this model to project forward in time to examine different paths in epidemic control after the initial surge is tamed and before the arrival of vaccines. Three very different control strategies are analyzed, leading to vastly different outcomes in terms of economic recovery and total infected population (or progress toward herd immunity). Our model, which is a version of the SEIQR model, is a time-dependent dynamical system with feedback-control. One of the main conclusions of this analysis is that the course of the epidemic is not entirely dictated by the virus: how the population responds to it can play an equally important role in determining the eventual outcome.
Highlights
The Covid-19 pandemic brought about renewed interest in epidemiological models
The mathematical framework we offer is flexible, exportable, and can be modified to describe a much larger class of epidemics than Covid-19
We focus on the population’s responses and consequences of the actions taken, modeling the time course of the epidemic as a dynamical system with feedback-control
Summary
The Covid-19 pandemic brought about renewed interest in epidemiological models. Medical research aside, vast numbers of modeling papers have been published since the start of the pandemic. The recent literature on Covid-modeling is vast, and as all this is happening in real time, it is not always easy to evaluate the impact of individual papers. Some of these papers have documented or analyzed events in specific regions of the world, others proposed mathematical models on how the infection spreads, yet others have tackled problems such as testing and herd immunity [1,2,3,4,5,6,7,8,9,10]. This paper contains a theoretical study of time evolutions of Covid-like epidemics from outbreak to vaccine arrival. We describe three different response strategies and track their performance over time
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