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

Kochanczyk, Marek; Grabowski, Frederic; Lipniacki, Tomasz

We constructed a simple Susceptible-Infected-Infectious-Excluded model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, r_E, and exclusion rate, r_E. The rates can be manipulated by non-therapeutic interventions and determine the basic reproduction number, R = r_C/r_E, and, together with τ, the daily multiplication coefficient at the early exponential phase, β. Initial β determines the reduction of r_C required to contain epidemic spread. In the long-term, we consider a scenario based on typical social behaviours, in which r_C first decreases in response to a surge of daily new cases, forcing people to self-isolate, and then slowly increases when people gradually accept higher risk. Consequently, initial abrupt epidemic spread is followed by a plateau and slow regression. This scenario, although economically and socially devastating, will grant time to develop, produce, and distribute a vaccine, or at least limit daily cases to a manageable number.