Global Stability of a Two-Scale Network Sir Delayed Epidemic Dynamic Model

The recent high rate of globalization of new disease strains and infectious agents at non-endemic zones is closely associated with complex human population structure and the large-scale inter-patch connections human transportations. The complexities in the human population structure create heterogeneities with respect to patch dwelling populations as well as endemic population structure. We present a multi-group SIRS dynamic epidemic process in the context of scale structured population. For simplicity we limit the scale to the value of two and define a multi-scale extension algorithm for the epidemic process. We investigate the global uniform asymptotic stability of the disease free equilibrium of the scale structured epidemic dynamic process and its impact on the emergence, propagation and resurgence of the disease. The presented results are demonstrated by numerical simulation results.