Seasonal Forcing in Stochastic Epidemic Models

We consider two types of stochastic epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. In this work, we demonstrate how to extend the theory to identify the optimal path to extinction when seasonality in the contact rate is included in the models.