A Time-Dependent SIRD Nonlinear Cross-Diffusion Epidemic Model: Multiscale Derivation and Computational Analysis

A time-dependent Susceptible-Infected-Recovered-Dead nonlinear cross-diffusion epidemic model is proposed in this chapter. This macro-scale model is derived from the kinetic theory model by multiscale approach, which leads to an equivalent system coupled the microscopic and macroscopic equations. Subsequently, numerical investigations to design asymptotic preserving scheme property are adopted and validated by various numerical tests. Finally, the numerical computational results of the proposed model are discussed in two-dimensional space using the finite volume method.