Endemic persistence or disease extinction: The effect of separation into sub-communities

Consider an infectious disease which is endemic in a population divided into several large sub-communities that interact. Our aim is to understand how the time to extinction is affected by the level of interaction between communities. We present two approximations of the expected time to extinction in a population consisting of a small number of large sub-communities. These approximations are described for an SIR epidemic model, with focus on diseases with short infectious period in relation to life length, such as childhood diseases. Both approximations are based on Markov jump processes. Simulations indicate that the time to extinction is increasing in the degree of interaction between communities. This behaviour can also be seen in our approximations in relevant regions of the parameter space.