论文标题
在反应扩散系统上对没有生命免疫力的传染病进行建模
On a Reaction-Diffusion System Modeling Infectious Diseases Without Life-time Immunity
论文作者
论文摘要
在本文中，我们研究了一种传染病的数学模型，例如 霍乱没有生命的免疫力。由于对易感，感染的人类宿主的迁移率不同，因此假定扩散系数不同。所得系统受具有不同扩散系数的强耦合反应扩散系统的控制。在已知数据的某些假设下建立了全球存在和唯一性。此外，当某些参数满足某些条件时，将获得溶液的全球渐近行为。这些结果扩展了文献中现有的结果。本文中使用的主要工具来自椭圆形和抛物线方程的精致理论。此外，使用{\ em apriori}估计值的能量法和Sobolev嵌入。本文中进行的分析可用于研究生物学和生态系统中的其他流行模型。
In this paper we study a mathematical model for an infectious disease such as Cholera without life-time immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction-diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behavior of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving {\em apriori} estimates. The analysis developed in this paper can be employed to study other epidemic models in biological and ecological systems.
