  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.
