Viruses competition in the genotype space

Cristina Leon,Vitaly Volpert,Vladimir Popov,V Volpert,F Syomin

doi:10.1051/itmconf/20203102002

Abstract

This paper is devoted to the study of persistence and evolution of two viruses taking into account virus mutation, reproduction, and genotype dependent mortality, either natural or determined by an antiviral treatment. The model describes the virus density distribution u(x; t) for the first virus and v(y; t) for the second one as functions of genotypes x and y considered as continuous variables and of time t. The model consists of a system of reaction-diffusion equations with integral terms characterizing virus competition for host cells. The analysis of the model shows the conditions of the existence of virus strains.

Highlights

Viruses are in a constant evolution owing to variation of their genetic structure as the result of the interaction of the replication, recombination or mutation [1]
This paper is devoted to the study of persistence and evolution of two viruses taking into account virus mutation, reproduction, and genotype dependent mortality, either natural or determined by an antiviral treatment
In this study we propose a mathematical model which considers the aforementioned processes that affects the concentration of virus in the host organism without taking into account the immune response, in the case of the existence of two viruses u, v in the host

Summary

Introduction

Viruses are in a constant evolution owing to variation of their genetic structure as the result of the interaction of the replication, recombination or mutation [1]. The concentration of virus in the host organism can be affected by its elimination, either by the immune response, virus natural death or some antiviral treatment. In [3], a model that describes the evolution of virus density depending on the genotype is introduced and the conditions for the existence of virus strains are determined. Theses equations describe the evolution of virus densities depending on the genotypes x and y respectively, considered as continuous variables and on time. The last term in the right-hand side of equation (1) describes virus natural death or its elimination by some antiviral treatment. We consider the virus strain as density distribution concentrated around some genotype value It is a non-negative solution of system (1) that decays at infinity. The detailed analysis of the reactiondiffusion type equations as well as the principles of formulating a mathematical model of virus infections and immunology are presented in [4] and [5]

Existence of stationary solutions

Discussion