Epidemic Spreading in a Social Network with Facial Masks wearing Individuals

In this paper, we present a susceptible-infected-recovered (SIR) model with individuals wearing facial masks and individuals who do not. The disease transmission rates, the recovering rates and the fraction of individuals who wear masks are all time dependent in the model. We develop a progressive estimation of the disease transmission rates and the recovering rates based on the COVID-19 data published by John Hopkins University. We determine the fraction of individual who wear masks by a maximum likelihood estimation, which maximizes the transition probability of a stochastic susceptible-infected-recovered model. The transition probability is numerically difficult to compute if the number of infected individuals is large. We develop an approximation for the transition probability based on central limit theorem and mean field approximation. We show through numerical study that our approximation works well. We develop a bond percolation analysis to predict the eventual fraction of population who are infected, assuming that parameters of the SIR model do not change anymore. We predict the outcome of COVID-19 pandemic using our theory.