TITLE:
The Global Analysis of a Stochastic Two-Scale Network Epidemic Dynamic Model with Varying Immunity Period
AUTHORS:
Divine Wanduku, G. S. Ladde
KEYWORDS:
Disease-Free Steady State, Stochastic Asymptotic Stability, Threshold Value, Positively Self Invariant Set, Lyapunov Functional Technique
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.5,
May
27,
2017
ABSTRACT: A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.