Stochastic Modeling of zoonotic diseases and estimating the mean time to disease extinction.

Eradicating infectious diseases remains a major priority for all public health initiatives because of the varied challenges such diseases pose to the human population and the world at large. The average time to disease extinction or the mean persistence time of a disease is an active focus in research because it measures the effort necessary to successfully eradicate the disease. While it is possible to directly calculate the mean persistence time, this approach becomes expensive when dealing with complex models or large population sizes, hence emphasizing the need for approximation methods. We focus on existing models such as the SIS$\kappa$ model and the Ebola Virus Disease (EVD) model which reflect our specific interest in zoonotic diseases. Using these models, we estimate the mean persistence time by running simulations and applying an approximation method known as the Wentzel-Kramers-Brillouin (WKB) approximation, which transforms a stochastic system into a Hamiltonian system, independent of population size. From these results, we are able to determine effective ways to eliminate diseases that follow this general dynamic.