A nonlinear cross-diffusion epidemic with time-dependent SIRD system: Multiscale derivation and computational analysis

Abstract: A nonlinear cross-diffusion epidemic with a time-dependent Susceptible-Infected-Recovered-Died system is proposed in this paper. This system is derived from 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 is developed and validated by various numerical tests. Finally, the numerical computational results of the proposed system are discussed in two dimensional space using the finite volume method.