Reaction–Diffusion Model of Coexistence of Viruses in the Space of Genotypes

Abstract

This work is devoted to the study of persistence and evolution of two viruses in the host organism taking into account characteristic aspects of viral dynamic such as virus mutation, replication, and genotype-dependent mortality, either natural or determined by an antiviral treatment. The proposed model consists of a system of nonlocal reaction–diffusion equations that describe the virus density distribution \(u(x,t)\) for the first virus and \(v\left(y,t\right)\) for the second one as functions of genotypes \(x\) and \(y\) considered as continuous variables, and of time \(t\). These equations contain two integral terms characterizing the nonlocal competition of viruses for host cells. Each virus strain is considered as density distribution concentrated around some average genotype value. The analysis of the model shows the conditions of the coexistence of virus strains in the host organism.