Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

¹ Department of Biosystems and Soft Matter, Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland.
² Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland.

^* Corresponding author: tlipnia@ippt.pan.pl

Received: 25 March 2020
Accepted: 5 April 2020

Abstract

We constructed a simple Susceptible−Exposed–Infectious–Removed model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, β, and exclusion rate, γ. The rates depend on nontherapeutic interventions and determine the basic reproduction number, R₀ = β/γ, and, together with τ, the daily multiplication coefficient in the early exponential phase, θ. Initial R₀ determines the reduction of β required to contain the spread of the epidemic. We demonstrate that introduction of a cascade of multiple exposed states enables the model to reproduce the distributions of the incubation period and the serial interval reported by epidemiologists. Using the model, we consider a hypothetical scenario in which β is modulated solely by anticipated changes of social behaviours: first, β decreases in response to a surge of daily new cases, pressuring people to self-isolate, and then, over longer time scale, β increases as people gradually accept the risk. In this scenario, initial abrupt epidemic spread is followed by a plateau and slow regression, which, although economically and socially devastating, grants time to develop and deploy vaccine or at least limit daily cases to a manageable number.