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首页> 外文期刊>Applied Mathematical Modelling >Adaptive dispersal effect on the spread of a disease in a patchy environment
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Adaptive dispersal effect on the spread of a disease in a patchy environment

机译：在斑驳的环境中对疾病传播的适应性扩散效应

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摘要

During outbreaks of a communicable disease, people intensely follow the media coverage of the epidemic. Most people attempt to minimize contact with others, and move themselves to avoid crowds. This dispersal may be adaptive regarding the intensity of media coverage and the population numbers in different patches. We propose an epidemic model with such adaptive dispersal rates to examine how appropriate adaption can facilitate disease control in connected groups or patches. Assuming dependence of the adaptive dispersal on the total population in the relevant patches, we derived an expression for the basic reproduction number R_0 to be related to the intensity of media coverage, and we show that the disease-free equilibrium is globally asymptotically stable if R_0<1, and it becomes unstable if R_0>1. In the unstable case, we showed a uniform persistence of disease by using a perturbation theory and the monotone dynamics theory. Specifically, when the disease mildly affects the dispersal of infectious individuals and rarely induces death, a unique endemic equilibrium exists in the model, which is globally asymptotically stable in positive states. Moreover, we performed numerical calculations to explain how the intensity of media coverage causes competition among patches, and influences the final distribution of the population.
机译：在传染病暴发期间，人们密切关注该流行病的媒体报道。大多数人试图尽量减少与他人的接触，并采取行动避免人群拥挤。关于媒体覆盖的强度和不同补丁中的人口数量，这种分散可以是自适应的。我们提出一种具有这种适应性扩散率的流行病模型，以研究适当的适应性如何能够促进相连群体或斑块中的疾病控制。假设在相关斑块中适应性扩散对总种群的依赖性，我们得出了一个基本繁殖数R_0的表达式，该表达式与媒体覆盖的强度有关，并且我们证明如果R_0的话，无病平衡在全局渐近稳定<1，并且如果R_0> 1则变得不稳定。在不稳定的情况下，我们通过使用扰动理论和单调动力学理论显示出一致的疾病持续性。具体而言，当疾病对感染者的散布产生轻微影响并且很少引起死亡时，模型中将存在唯一的地方性平衡，在平衡状态下该平衡是全局渐近稳定的。此外，我们进行了数值计算，以解释媒体报道的强度如何导致补丁之间的竞争，并影响人口的最终分布。

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