SDE SIS epidemic model with demographic stochasticity and varying population size
SDE SIS epidemic model with demographic stochasticity and varying population size
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DOI：
10.1016/j.amc.2015.11.094
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
D. Greenhalgh;Yanfeng Liang;X. Mao
中科院分区：
文献类型：
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作者：
D. Greenhalgh;Yanfeng Liang;X. Mao
本文研究了具有人口统计随机性的二维随机微分方程（SIS）传染病模型，其中出生和死亡被视为随机过程，人均疾病接触率依赖于人口规模.首先，我们看看总人口规模的非线性模型，并证明存在唯一的非负解。然后，我们看看在二维的CRISSIS模型，并证明存在唯一的非负解，这是有界的总人口规模。此外，我们还证明了在有限时间内，感染者的数量和易感者的数量几乎必然灭绝。最后，我们支持我们的分析结果与数值模拟使用理论和现实的疾病参数值。
In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.