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Well-posedness for a diffusion–reaction compartmental model simulating the spread of COVID-19
Mathematical Methods in the Applied Sciences ; 2023.
Article in English | Scopus | ID: covidwho-2250550
ABSTRACT
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 paper by Viguerie et al (2020). 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. © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.
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Full text: Available Collection: Databases of international organizations Database: Scopus Language: English Journal: Mathematical Methods in the Applied Sciences Year: 2023 Document Type: Article

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Full text: Available Collection: Databases of international organizations Database: Scopus Language: English Journal: Mathematical Methods in the Applied Sciences Year: 2023 Document Type: Article