Before revision:  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.
After revision:  Following a mean field approach that models individuals like molecules in a well-mixed solution, one derives 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.