On the Mathematical Analysis of the Stochastic Age-structured Infectious Model

抄録

The stability of the stochastic age-structured infectious model is studied in this paper. At present, we have still various kinds of the infectious disease threats including Corona virus disease, influenza and monkeypox. Hence, the analysis of infection diseases plays an important role in the modern society. In the past, a great deal of research of infectious diseases has been performed using various kinds of mathematical tools and models. Most of the conventional research is based on the deterministic mathematical tools and models. However, 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, the parameters of the population dynamics such as infection, recovery, birth and death rates depend on 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 steady state of the stochastic infectious models, we consider the stability of the stochastic infectious models and derive the sufficient conditions for the steady state to be stable by using the stochastic Lyapunov theorem.