The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model
The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model
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媒体报道对随机 SIS 流行病模型阈值动态的影响
DOI：
10.1016/j.physa.2018.08.113
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发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
Sanling Yuan
中科院分区：
文献类型：
--
作者：
Yu Zhao;Liping Zhang;Sanling Yuan
媒体报道是控制传染病的重要措施之一，但媒体报道对随机环境下疾病传播的影响仍需进一步研究。在这里，我们提出了一个结合媒体报道和环境波动的随机易感者-感染者-易感者（SIS）流行病模型。利用费勒检验和随机比较原理，我们建立了随机基本再生数R 0 s，完全决定了疾病在人群中是否持续存在。如果R 0 s≤1，疾病就会灭绝；如果R 0 s=1，该疾病也有概率走向灭绝，这在已知文献中尚未有报道。如果R 0 s> 1，则疾病将随机持续。此外，还得出了模型平稳分布的存在性及其遍历性。基于实例的数值模拟支持了理论结果。有趣的发现是：（i）环境波动可能显着影响疾病的阈值动态行为和不同规模人群的波动；（ii）媒体报道在影响低强度噪声环境下疾病的平稳分布方面发挥着重要作用。
Media coverage is one of the important measures for controlling infectious diseases, but the effect of media coverage on diseases spreading in a stochastic environment still needs to be further investigated. Here, we present a stochastic susceptible–infected–susceptible (SIS) epidemic model incorporating media coverage and environmental fluctuations. By using Feller’s test and stochastic comparison principle, we establish the stochastic basic reproduction number R 0 s, which completely determines whether the disease is persistent or not in the population. If R 0 s≤ 1, the disease will go to extinction; if R 0 s= 1, the disease will also go to extinction in probability, which has not been reported in the known literatures; and if R 0 s> 1, the disease will be stochastically persistent. In addition, the existence of the stationary distribution of the model and its ergodicity are obtained. Numerical simulations based on real examples support the theoretical results. The interesting findings are that (i) the environmental fluctuation may significantly affect the threshold dynamical behavior of the disease and the fluctuations in different size scale population, and (ii) the media coverage plays an important role in affecting the stationary distribution of disease under a low intensity noise environment.
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