2019 Volume 2019 Pages 111-116
This paper is concerned with the stability analysis of the stochastic age-structured infectious model. We have been faced with a threat of the infectious disease even in the modern society with a high medical technology. Hence, infection prevention and control of epidemic are cited as one of the important social problems. Until now, interesting and impactful research of infectious diseases has been performed using various kinds of mathematical models. However, most of the research is based on the deterministic model and the age-structure has not been taken into account. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection, the recovery rates and the vaccination effect. Moreover, there exists the difference in the transmission intensity of infection by age. Taking these facts into consideration, we propose the stochastic age-structured infectious model. Since the spread of infection has reference to the stability of the disease-free steady state (DFS) of the stochastic infectious models, we analyze the stability of the DFS by using the stochastic Lyapunov theorem.
