A feedback SIR (fSIR) model highlights advantages and limitations of infection-based social distancing

Transmission rates in epidemic outbreaks vary over time depending on the societal and government response to infections and mortality data, as evidenced in the course of the COVID-19 pandemic. Following a mean field approach that models individuals like molecules in a well-mixed solution, I derive a modified SIR model in which the average daily contacts between susceptible and infected population are reduced based on the known infection levels, capturing the effects of social distancing policies. This approach yields a time-varying reproduction number that is continuously adjusted based on infection information through a negative-feedback term that is equivalent to Holling type II functions in ecology and Hill functions in chemistry and molecular biology. This feedback-adjustment of the transmission rate causes a structural reduction in infection peak, and simulations indicate that such reduction persists even in the presence of information delays. Simulations also show that a distancing policy based on infection data may substantially extend the duration of an epidemic. If the distancing rate is linearly proportional to infections, this model adds a single parameter to the original SIR, making it useful to illustrate the effects of social distancing enforced based on awareness of infections.