Global Analysis of a Stochastic Two-scale Network Human Epidemic Dynamic Model With Varying Immunity Period

Presented at AMS Special Session on “Stochastic Analysis of Stochastic Differential Equations and Stochastic Partial Differential Equations”, 119th Annual Meeting of the American Mathematical Society (AMS)

The recent rapid spread of infectious diseases of humans is closely associated with the spatial complex human population structure and the underlying large-scale inter-patch connection human transportation. Furthermore, the fluctuations in disease endemicity within patch dwelling populations are closely related with the hereditary features of the disease. We present a stochastic SIR delayed dynamic epidemic model for a two-scale dynamic structured population. The disease confers varying time infection acquired immunity to recovered individuals. The varying time delay period accounts for the time-lag during which recovered individuals with conferred infection acquired immunity become susceptible. We investigate the stochastic asymptotic stability of the disease free equilibrium of the two-scale structured mobile dynamic population, and further examine the impacts on the eradication of the disease.