一类具有非线性发病率的随机SIRS模型的渐近行为

Threshold of a Stochastic SIRS Epidemic Model with Nonlinear Incidence

讨论了一类具有非线性发病率的随机SIRS流行病模型,得到了随机模型的一个阈值决定着疾病的灭绝和持续,与相应的确定性模型相比,受白噪声影响的随机模型的阈值小于确定性模型的基本再生数。当噪声较小时,随机模型存在一个无病吸收集,即疾病会以概率1灭绝;当噪声较大时,会抑制疾病的流行。计算机模拟验证了这些结果。

A stochastic SIRS type epidemic model with nonlinear incidence is discussed.We obtain a threshold of the stochastic model which determines the extinction and persistence of the epidemic.Compared with the corresponding deterministic model,the threshold of the stochastic model affected by white noise is smaller than the basic reproduction number of the deterministic model.When the noise is small,the stochastic model exists a disease-free absorbing set which implies that the disease dies out with probability one.When the noise is large,it will suppress the epidemic from prevailing.These results are illustrated by computer simulations.