具有一般发生率的随机SIRS模型的灭绝与持久性
Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate
摘要：
本文考虑了一类具有一般发生率的同时受白噪声和色噪声干扰的随机SIRS模型。我们确定阈值$λ$，用于分类疾病的灭绝和持久性。特别地，$λ<0$意味着无病$(K, 0, 0)$是全局渐近稳定的，即，疾病最终会消失。如果使用$λ>0$，则流行病具有很强的随机性和永久性。我们的结果被认为是对\cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}结果的一个重要推广和改进。
英文摘要：
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $λ$ that is used to classify the extinction and permanence of the disease. In particular, $λ<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $λ>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in \cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}.
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