Virus models in complex frameworks: Towards modeling space patterns of SARS-CoV-2 epidemics

Abstract

This paper deals with the micro–macro-derivation of virus models coupled with a reaction–diffusion system that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [N. Bellomo, K. Painter, Y. Tao and M. Winkler, Occurrence versus absence of taxis-driven instabilities in a May–Nowak model for virus infection, SIAM J. Appl. Math. 79 (2019) 1990–2010; N. Bellomo and Y. Tao, Stabilization in a chemotaxis model for virus infection, Discrete Contin. Dyn. Syst. S 13 (2020) 105–117], on a survey and a critical analysis of some phenomenological models known in the literature. The second part shows how a Hilbert type can be developed to derive models at the macro-scale from the underlying description delivered by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models of various virus models coupled with the reaction–diffusion systems. Then, a forward look to research perspectives is proposed.