Abstract
This paper focuses on stochastic infectious disease models in the context of biological problems. Stochastic infectious disease models with mean-reverting processes are studied, and the model studied is a stochastic SIS infectious disease model with mean-reverting birth mortality[1-7]. The persistence and extinction of diseases are discussed in the context of the infectious disease mode[8-11]l, giving thresholds such that if the threshold is less than 1, the disease becomes extinct with probability 1, and if the threshold is greater than 1, the disease persists with probability 1 in the mean sense. From this analysis, we conclude that the greater the intensity of the fluctuation, the faster the disease goes extinct, while the smaller the intensity of the fluctuation, the greater the number of infectious diseases.
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