Quantifying the effect of synchrony on the persistence of infectious diseases in a metapopulation

Global persistence of infectious diseases is a big problem for epidemiologists. There are a lot of reasons to answer why many communicable diseases still exist and have been developed in more dangerous form. The asynchrony and the recolonization among subpopulations are two key reasons pointed out. How to solve these problems is still an open question. We study here the combined effects of forcing phase heterogeneity in the seasonally forced contact rate on global persistence of disease. We carry out an exploitation of stochastic dynamics in a susceptible-exposed-infectious-recovered (SEIR) model of the spread of infectious diseases in a metapopulation of n subpopulations. Starting with continuous-time Markov description of the model of deterministic equation, the direct method of Gillespie(1977) [1] in the class of Monte-Carlo simulation methods allows us to simulate exactly the spread of disease with the SEIR model. Our finding shows that the disease persistence in the metapopulation is characterized as an exponential survival model on data simulated by the stochastic model. How bigger the forcing phase heterogeneity becomes, and how smaller the extinction rate gets.