论文标题
适当的扩散反应隔室模型，模拟Covid-19的扩散
Well-posedness for a diffusion-reaction compartmental model simulating the spread of COVID-19
论文作者
论文摘要
本文涉及易感暴露感染的（SEIR）数学模型的扩散反应系统的良好性。该模型是根据四个非线性偏微分方程和非线性扩散的编写，具体取决于SEIR人群的总量。该模型旨在描述Covid-19大流行的时空传播，并且是最近引入，讨论和测试的变体[A. Viguerie等人，《连续力学框架：Covid-19，数学分析》和《数值研究》中的扩散反应隔室模型，计算。机械。 66（2020）1131-1152]。在这里，我们处理由此产生的库奇 - 尼曼问题的数学分析：在相当通用的环境中证明了解决方案的存在，并采用了合适的时间离散程序。值得一提的是，通过仔细利用系统结构来显示离散解决方案的统一界限。相对于时间步的统一估计和通过限制允许完成存在的证明。然后，提供了两个唯一性定理，一个在恒定扩散系数的情况下，另一个用于更常规的数据，并结合解决方案的规律性结果。
This paper is concerned with the well-posedness of a diffusion-reaction system for a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with nonlinear diffusions, depending on the total amount of the SEIR populations. The model aims at describing the spatio-temporal spread of the COVID-19 pandemic and is a variation of the one recently introduced, discussed and tested in [A. Viguerie et al, Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study, Comput. Mech. 66 (2020) 1131-1152]. Here, we deal with the mathematical analysis of the resulting Cauchy-Neumann problem: the existence of solutions is proved in a rather general setting and a suitable time discretization procedure is employed. It is worth mentioning that the uniform boundedness of the discrete solution is shown by carefully exploiting the structure of the system. Uniform estimates and passage to the limit with respect to the time step allow to complete the existence proof. Then, two uniqueness theorems are offered, one in the case of a constant diffusion coefficient and the other for more regular data, in combination with a regularity result for the solutions.
