A stochastic vector-borne epidemic model: Quasi-stationarity and extinction

We consider a stochastic model describing the spread of a vector borne disease in a community where individuals (hosts and vectors) die and new individuals (hosts and vectors) are born. The time to extinction of the disease, TQ, starting in quasi-stationary (conditional on non extinction) is studied. Properties of the limiting distribution are used to obtain an approximate expression for E(TQ), the mean-parameter in the exponential distribution of the time to extinction, for a finite population. It is then investigated numerically and by means of simulations how E(TQ) and its approximations depend on the different model parameters.