Multiscale Derivation of a Time-Dependent SEIRD Reaction–Diffusion System for COVID-19

Abstract

A time-dependent Susceptible-Exposed-Infectious-Recovered-Died reaction–diffusion system for the virus pandemic is proposed in this chapter. The macroscopic model is derived from the underlining description delivered by a kinetic theory model. The approach is based on a multiscale decomposition that leads to an equivalent formulation of the kinetic theory model, which couples the microscopic equations with the macroscopic equations. Subsequently, a numerical asymptotic preserving scheme to solve the equivalent formulation is developed and validated by various numerical tests.