A Path to the End of COIVD-19 - a Mathematical Model

In this work we use mathematical modeling to describe one possible route to the end of COVID-19, which does not feature either vaccination or herd immunity. We consider a region where the following conditions hold true : (a) there is no influx of cases from the outside, (b) there is extensive social distancing, though not necessarily a full lockdown, so that mass transmission events do not occur, and (c) testing capacity is high relative to the actual number of new cases per day. These conditions can make it possible for the region to initiate the endgame phase of epidemic management, wherein the virus is slowly starved of new targets through a combination of social distancing, sanitization, contact tracing and extensive testing. The dynamics of the cases in this regime is governed by a single-variable first order linear delay differential equation, whose stability criterion can be obtained explicitly. Analysis of the equation can tell us which social restrictions may be relaxed during the endgame, and which may not. For example, in an academic institution, a small research group might be allowed to meet in person once a week while classroom instruction should remain fully suspended. If the endgame can be played out for a long enough time, we claim that the disease can eventually get completely contained without affecting a significant fraction of the region9s population. We present estimates of the duration for which the epidemic is expected to last, finding an interval of approximately 5-15 weeks after the endgame strategy is initiated.