具有群体作用和小迁移率的SIS传染病扩散模型的总体分布
Novel Spatial Profiles of Population Distribution of Two Diffusive SIS Epidemic Models with Mass Action Infection Mechanism and Small Movement Rate for the Infected Individuals
摘要：
本文研究了具有$SI$形式的群体作用传染机制的两个SIS传染病反应扩散模型，研究了当传染病个体的移动速率被限制为较小时，种群总体分布的空间分布.结果表明，对于总种群数为常数的模型，易感种群总是收敛于一个正的常数，该常数实际上是相关风险函数的最小值;当最高风险点至少包含一个区间时，感染种群要么集中在孤立的最高风险点，要么只聚集在最高风险区间.与此形成鲜明对比的是，对于由易感个体的招募和感染个体的死亡引起的总人口数变化的模型，我们的结果表明，除非相关的风险函数是常数，否则易感人口收敛于一个非常数的正函数，而感染人口可能只集中在一些孤立的最高风险点，或者至少聚集在最高风险位置的邻域中，或者占据整个栖息地，这取决于相关风险函数的行为，甚至取决于其在最高风险位置处的平滑度。进行数值模拟，以支持和补充我们的理论研究结果。
英文摘要：
In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals is restricted to be small. For the model with a constant total population number, our results show that the susceptible population always converges to a positive constant which is indeed the minimum of the associated risk function, and the infected population either concentrates at the isolated highest-risk points or aggregates only on the highest-risk intervals once the highest-risk locations contain at least one interval. In sharp contrast, for the model with a varying total population number which is caused by the recruitment of the susceptible individuals and death of the infected individuals, our results reveal that the susceptible population converges to a positive function which is non-constant unless the associated risk function is constant, and the infected population may concentrate only at some isolated highest-risk points, or aggregate at least in a neighborhood of the highest-risk locations or occupy the whole habitat, depending on the behavior of the associated risk function and even its smoothness at the highest-risk locations. Numerical simulations are performed to support and complement our theoretical findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
