论文标题
非线性反应扩散系统建模传染病的渐近分析
Asymptotic Analysis for a Nonlinear Reaction-Diffusion System Modeling an Infectious Disease
论文作者
论文摘要
在本文中，我们研究了一种非线性反应扩散系统，该系统模拟了由细菌（例如霍乱）引起的传染病。该模型中的重要特征之一是，一定部分被回收的人类宿主可能会失去终生免疫力，并可能再次感染。该模型中的另一个重要特征是，允许每个物种的迁移率依赖于位置和时间。假定整个种群对细菌敏感，该模型是强烈耦合的非线性反应扩散系统。我们证明，在某些自然条件下，在模型参数和给定数据的某些自然条件下，非线性系统在任何空间维度上具有独特的解决方案。此外，严格进行了解决方案的长期行为和稳定性分析。特别是，我们表征了有关所有稳态解决方案的稳定性或不稳定性的可变参数的精确条件。这些新结果为文献中提出的几个开放问题提供了答案。
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human hosts may lose a lifetime immunity and could be infected again. Another important feature in the model is that the mobility for each species is allowed to be dependent upon both the location and time. With the whole population assumed to be susceptible with the bacteria, the model is a strongly coupled nonlinear reaction-diffusion system. We prove that the nonlinear system has a unique solution globally in any space dimension under some natural conditions on the model parameters and the given data. Moreover, the long-time behavior and stability analysis for the solutions are carried out rigorously. In particular, we characterize the precise conditions on variable parameters about the stability or instability of all steady-state solutions. These new results provide the answers to several open questions raised in the literature.
