具有非单调发病率的随机SIS模型的持续性与灭绝性

Persistence and Extinction of a Stochastic SIS Epidemic Model with Nonmonotone Incidence rate

讨论了一类具有非单调发病率的随机SIS模型．主要贡献在两个方面．在数学上，应用随机分析技术证明了R0^s可以作为随机模型的阈值．当R0^s〈1时，随机模型存在一个无病的吸引集，即疾病会以概率1灭绝．当R0^s〉1时，疾病是随机持续生存的．在流行病学上，结果表明环境噪声可以抑制疾病的爆发，可以为疾病的预防和控制提供一些参考．

A stochastic SIS type epidemic model with nonmonotone incidence rate is investigated in this paper. The contribution of this study lies in two aspects. Mathematically, by applying the technique of stochastic analysis, we prove that R~ can be the threshold of stochastic model. Whenever R0^s 〈 1, the stochastic model exists a disease-free absorbing set which implies that the disease dies out with probability one. Whenever R0^s 〈 1, the disease is stochastically persistent. Epidemiologically, we find that environmental noise can suppress the outbreak of disease, which can provide some useful suggestions to prevent and control disease.