SIS and SIR Epidemic Models Under Virtual Dispersal.
SIS and SIR Epidemic Models Under Virtual Dispersal.
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DOI：
10.1007/s11538-015-0113-5
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发表时间：
2015-11
影响因子：
3.5
通讯作者：
Perrings C
中科院分区：
文献类型：
--
作者：
Bichara D;Kang Y;Castillo-Chavez C;Horan R;Perrings C
我们开发了一个多组的流行病框架，通过虚拟分散的感染风险是一个功能的停留时间和当地的环境风险。这种新的方法消除了需要定义和测量接触率，在传统的多组传染病模型与异质混合。我们将这种方法应用到一个一般的n-补丁SIS模型，其基本再生数R 0作为补丁驻留时间矩阵的函数计算。我们的分析表明，当斑块是强连通时，所得到的n斑块SIS模型具有鲁棒动力学特性：当R 0> 1时，存在唯一的全局稳定的地方病平衡点，而当R 0 ≤ 1时，无病平衡点是全局稳定的.进一步的分析表明，由驻留时间矩阵描述的扩散行为对单个斑块水平上的疾病动态具有深远的影响，其结果是适当的扩散行为沿着当地环境风险可以促进或消除特定斑块中的地方病。我们的工作突出了停留时间矩阵的影响，如果补丁不是强连接。我们的框架可以推广到其他地方病和疾病爆发模型。作为一个例子，我们将我们的框架应用到两个补丁SIR单次爆发的流行病模型，其中疾病入侵的过程连接到最终的流行病规模关系。我们还探讨了疾病流行率驱动的决策的影响，使用现象学建模方法，以对比疾病动力学的恒定与状态依赖性疾病的作用。
We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number R0 is computed as a function of a patch residence-times matrix ℙ. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: there is a unique globally stable endemic equilibrium when R0 > 1 while the disease free equilibrium is globally stable when R0 ≤ 1. Our further analysis indicates that the dispersal behavior described by the residence-times matrix ℙ has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence times matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease prevalence driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state dependent ℙ on disease dynamics.