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

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 _C , 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.