  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.
