Vectorborne Diseases: a Generalized Scale Structured Network Stochastic Epidemic Dynamic Model

Presented at Disease Dynamics Seminars, College of Public Health, Georgia Southern University

Link to Program: https://sites.google.com/a/georgiasouthern.edu/fung/disease-dynamics-seminars

A stochastic epidemic dynamic model for vector-borne diseases in network structured populations involving two hierarchic levels (two-scales) is presented. Infected persons change state from Susceptible to Infectious and then to Removal, and back to Susceptible (SIRS). The delay in the epidemic dynamic process owing to the incubation the disease is incorporated into the dynamic system as a random process. Furthermore, the disease dynamics presented is influenced by fluctuations in the disease transmission process as well as the two-scale human mobility process. The threshold conditions for disease eradication at three human-vector contact levels in the two-scale population are computed, and the results for the long -term (asymptotic) stochastic stability of the steady states (equilibria) of the system derived are presented. Moreover the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.