一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

Abstract

Abstract: In this paper, a stochastic susceptible-infected-susceptible (SIS) epidemic model with nonlinear incidence rate is considered to investigate the effect of environment fluctuation on the transmission threshold dynamical behaviors. By using Feller's test and stochastic comparison principle, we obtain the stochastic basic reproduction number R₀^s, which determined whether the disease persistent or not. If R₀^s<1, the disease will go to extinction. If R₀^s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures. In addition, if R₀^s>1, the disease will stochastic persistence and the scale range estimation of spread is presented eventually. Finally, numerical simulations are carried out to support the theoretical results. According to the actual parameter, it illustrated the environmental fluctuation have different effect on different size of group.

Key words: Stochastic SIS epidemic model, Feller's test, Basic reproduction number, Threshold dynamical behaviors

CLC Number:

O211.6

Zhang Liping, Zhao Yu, Yuan Sanling. Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate[J].Acta mathematica scientia,Series A, 2018, 38(1): 197-208.

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References

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Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

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