Expected Time to Extinction of SIS Epidemic Model Using Quasy Stationary Distribution

Abstract: We study that the breakdown of epidemic depends on some parameters, that is expressed in epidemic reproduction ratio number. It is noted that when $R_0 $ exceeds 1, the stochastic model have two different results. But, eventually the extinction will be reached even though the major epidemic occurs. The question is how long this process will reach extinction. In this paper, we will focus on the Markovian process of SIS model when major epidemic occurs. Using the approximation of quasi--stationary distribution, the expected mean time of extinction only occurs when the process is one step away from being extinct. Combining the theorm from Ethier and Kurtz, we use CLT to find the approximation of this quasi distribution and successfully determine the asymptotic mean time to extinction of SIS model without demography.