文章基本信息

标题：An SEIRS epidemic model with stochastic transmission
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作者：Peter J Witbooi
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：109
DOI：10.1186/s13662-017-1166-6
语种：English
出版社：Hindawi Publishing Corporation
摘要：For an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the existence of global positive solutions. For sufficiently small values of the perturbation parameter, we prove the almost surely exponential stability of the disease-free equilibrium whenever a certain invariant R σ $\mathcal{R}_{\sigma}$ is below unity. Here R σ < R $\mathcal{R}_{\sigma}< \mathcal{R}$ , the latter being the basic reproduction number of the underlying deterministic model. Biologically, the main result has the following significance for a disease model that has an incubation phase of the pathogen: A small stochastic perturbation on the transmission rate from susceptible to infectious via the latent phase will enhance the stability of the disease-free state if both components of the perturbation are non-trivial; otherwise the stability will not be disturbed. Simulations illustrate the main stability theorem.
关键词：SEIRS model ; stochastic transmission ; almost sure exponential stability