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

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 withτ, the daily multiplication coefficient in the early exponential phase,θ. InitialR0determines the reduction ofβrequired 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 whichβis modulated solely by anticipated changes of social behaviours: first,βdecreases in response to a surge of daily new cases, pressuring people to self-isolate, and then, over longer time scale,βincreases 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.