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

TL;DR

This paper introduces a multiscale derived nonlinear cross-diffusion SIRD epidemic model with time dependence, and develops numerical schemes validated through 2D computational experiments.

Contribution

It presents a novel multiscale derivation of a nonlinear cross-diffusion epidemic model with time-dependent parameters and provides a validated numerical scheme for its simulation.

Findings

Successful derivation from kinetic theory

Development of an asymptotic preserving numerical scheme

Effective 2D computational analysis using finite volume method

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.