PERMANENCE AND EXTINCTION OF A NONAUTONOMOUS STAGE-STRUCTURED EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAY

In this paper, we have considered a nonautonomous stage-structured epidemic model having two stages of the period of infection according to the progressing process of some infectious diseases (e. g. Chagas' disease, hepatitis C, etc.) with varying total population size and distributed time delay to become infectious. The infected persons in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected persons. We have introduced some new threshold values R-0 and R* and further obtained that the disease will be permanent when R-0 > 1 and the disease will be going to extinct when R* < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.