Maximum entropy method for estimating the reproduction number: An investigation for COVID-19 in China

The key parameter that characterizes the transmissibility of a disease is the reproduction number R . If it exceeds 1, the number of incident cases will inevitably grow over time, and a large epidemic is possible. To prevent the expansion of an epidemic, R must be reduced to a level below 1. To estimate the reproduction number, the probability distribution function of the generation interval of an infectious disease is required to be available; however, this distribution is often unknown. In this letter, given the incomplete information for the generation interval, we propose a maximum entropy method to estimate the reproduction number. Based on this method, given the mean value and variance of the generation interval, we first determine its probability distribution function and in turn estimate the real-time values of reproduction number of COVID-19 in China. By applying these estimated reproduction numbers into the susceptible-infectious-removed epidemic model, we simulate the evolutionary track of the epidemic in China, which is well in accordance with that of the real incident cases. The simulation results predict that China’s epidemic will gradually tend to disappear by May 2020 if the quarantine measures can continue to be executed.