A Scale-Structured Network Stochastic Epidemic dynamic model with varying Incubation Period

Presented at AMS Special Session on Fractional, Stochastic, and Hybrid Dynamic Systems with Applications , 120th Annual Meeting of the American Mathematical Society (AMS)

We present a stochastic SIR delayed epidemic dynamic model for a vector-born disease in a two-scale structured population. The distributed time delay accounts for the varying incubation period of the infectious agent in the vector. Furthermore, the infectious vector population is proportional to the infectious human population present at the onset of the incubation period. In addition, the disease dynamics is influenced by random environmental perturbations leading to variability in the disease transmission process. We investigate the stochastic asymptotic stability of the disease free equilibrium and verify the impact on the emergence, propagation and resurgence of the disease. The presented results are demonstrated by numerical simulation results.