Well‐posedness for a diffusion–reaction compartmental model simulating the spread of COVID‐19

This paper is concerned with the well-posedness of a diffusion-reaction system for Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. model written in terms four nonlinear partial differential equations diffusions, depending on total amount SEIR populations. The aims at describing spatio-temporal spread COVID-19 pandemic and variation one recently introduced, discussed tested [A. Viguerie et al, Diffusion-reaction compartmental models formulated continuum mechanics framework: application to COVID-19, analysis, numerical study, Comput. Mech. 66 (2020) 1131-1152]. Here, we deal analysis resulting Cauchy-Neumann problem: existence solutions proved rather general setting suitable time discretization procedure employed. It worth mentioning that uniform boundedness discrete solution shown by carefully exploiting structure system. Uniform estimates passage limit respect step allow complete proof. Then, two uniqueness theorems are offered, case constant diffusion coefficient other more regular data, combination regularity result solutions.