Long-time behaviour of a perturbed SIR model by white noise
Long-time behaviour of a perturbed SIR model by white noise
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DOI：
10.3934/dcdsb.2013.18.1873
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发表时间：
2013-05
影响因子：
1.2
通讯作者：
Yuguo Lin;D. Jiang
中科院分区：
文献类型：
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作者：
Yuguo Lin;D. Jiang
本文考虑一类疾病传播系数为扰动的随机SIR模型。我们提出了疾病指数灭绝的充分条件。在持久性的情况下，我们分析的解决方案的分布的密度的长时间的行为。我们将证明在适当的条件下，解的密度可以在L^1 $内收敛到不变密度。同时我们也得到了不变密度的支持。特别地，当白色噪声的强度相对较小时，我们发现了一个新的阈值的流行病发生。
In this paper, we consider a stochastic SIR model with perturbed disease transmission coefficient. We present sufficient conditions for the disease to extinct exponentially. In the case of persistence, we analyze long-time behaviour of densities of the distributions of the solution. We will prove that the densities of the solution can converge in $L^1$ to an invariant density under appropriate conditions. Also we find the support of the invariant density. Specially, when the intensity of white noise is relatively small, we find a new threshold for an epidemic to occur.