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

Yong Tao

simulate the evolutionary track of this epidemic. To estimate the reproduction number , the probability distribution function of the generation interval of an infectious disease, ( ), is required to be available [5, [9] [10] [11] [12] ; however, this distribution is often unknown. In the existing literature, many scholars used exponential distribution [5] , normal distribution [5] , Weibull distribution [9, 10] , and Gamma distribution [3, 12] to approximate ( ). Theoretically, to use these distributions to approximate ( ), one needs to know enough information about symptom onsets of all cases, namely, large sample cases for . Regarding the incomplete information, one also applied the Monte-Carlo method [4] and Bayesian statistical inference [11] to estimating ( ). However, thus far, there is scant literature to discuss the potential application of the maximum entropy method (MaxEnt) [13] [14] [15] in estimating the reproduction number. Our letter fills this gap. In the statistical inference, MaxEnt is a powerful tool of predicting probability distributions. The main idea of MaxEnt is to estimate a target probability distribution by finding the probability distribution of maximum entropy, subject to a set of constraints that represent our incomplete information for the target distribution [13] .