Impact of the constant and time-varied contact rate on COVID-19 pandemic dynamic

We constructed a simple Susceptible-Infected-Infectious-Excluded model of the spread of COVID-19. The model is parametrized only by the average incubation period \tau 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 \tau the daily multiplication coefficient \beta of epidemic spread in its early exponential phase. In turn, initial \beta determines the reduction of r_C required to contain epidemic growth. In long-term, we consider scenario based on typical social behaviors 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 are accepting higher risk. Consequently, initial abrupt epidemic spread is followed by a plateau and slow reversion. This scenario, although economically and socially devastating, will grant time to develop, produce, and distribute vaccine, or at least limit daily cases to manageable number.

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