Bayesian parameter inference for stochastic SIR epidemic model with hyperbolic diffusion

This paper is concerned with the Bayesian estimation parameters of the stochastic SIR (Susceptible-Infective-Removed) epidemic model from the trajectory data. Specifically, the data from the count of both infectives and susceptibles is assumed to be available on some time grid as the epidemic progresses. The diffusion approximation of the appropriate jump process is then used to estimate missing data between every pair of observation times. If the time step of imputations is small enough, we derive the posterior distributions of the infection and recovery rates using the Milstein scheme. The paper also presents Markov-chain Monte Carlo (MCMC) simulation that demonstrates that the method provides accurate estimates, as illustrated by the synthetic data from SIR epidemic model and the real data.