抄録
An infectious disease is still a menace to our health even in high-technogical and advanced information society. A prevention of prevalence of the infectious disease is one of important problems in epidemiology. In such a problem, the mathematical model which describes the spread of the infectious disease has a very important role in the prediction and the analysis of prevalence of the infectious disease. In this paper, we study the modeling of the infectious disease in populations consisting of four populations: susceptible, infective, recovered and vaccinated ones. Noting that the real infectious disease contains some kinds of random fluctuations caused by changes in the environment and the weather, we propose the stochastic infectious model. By using the proposed stochastic model, we analyze the influence of the random fluctuation and vaccination on the spread of the infectious disease by numerical simulations.
