Two-Scale Stochastic Network Dynamic Epidemic Models

The non-uniform global spread of emergent infectious diseases of humans is closely interrelated with the large-scale structure of the human population, and the human mobility process in the population structure. For a given spatial scale of a human meta-population, every patch can be decomposed into sub patches, for example, homes, neighborhoods, towns, counties and countries, etc. And all sub patches are interlinked through a human transport network. The mobility dynamic process creates heterogeneities within the large-scale population structure with respect to the dwelling population of a given patch, namely: citizen, permanent resident, visitor, etc. The mobile population becomes the vector for the disease. We present an SIRS stochastic dynamic epidemic process in a two scale structured population. The disease confers two kinds of recovery: permanent recovery from infection and recovery from infection with a direct transfer back into the susceptible population immediately after infection. The variability caused by the fluctuating environment is assumed to manifest mainly in the transmission process. We investigate the role of population scale structure, the mobility process and environmental fluctuations on the emergence, propagation and resurgence of the disease.