Threshold Dynamics and Competitive Exclusion in a Virus Infection Model with General Incidence Function and Density-Dependent Diffusion

Xiaosong Tang,Jianping Yang,Zhiwei Wang

doi:10.1155/2020/4923856

Abstract

In this paper, we investigate single-strain and multistrain viral infection models with general incidence function and density-dependent diffusion subject to the homogeneous Neumann boundary conditions. For the single-strain viral infection model, by using the linearization method and constructing appropriate Lyapunov functionals, we obtain that the global threshold dynamics of the model is determined by the reproductive numbers for viral infection ℛ0. For the multistrain viral infection model, we have discussed the competitive exclusion problem. If the reproduction number ℛi for strain i is maximal and larger than one, the steady state Ei corresponding to the strain i is globally stable. Thus, competitive exclusion happens and all other strains die out except strain i. Meanwhile, we can prove that the single-strain and multistrain viral infection models are well posed. Furthermore, numerical simulations are also carried out to illustrate the theoretical results, which is seldom seen in the relevant known literatures.

Highlights

Nowadays, more and more people in the world are dying of various diseases such as AIDS, avian influenza, cholera, Ebola, and Zika virus
From eorem 7, we can know that infection-free equilibrium E30 of model (62) is globally asymptotically stable, which implies that all viral strains die out. ese facts are numerically confirmed in
We investigate the global threshold dynamics in single-strain viral infection models (1) and competitive exclusion in multistrain viral infection models (7) under the homogeneous Neumann boundary conditions

Summary

Introduction

More and more people in the world are dying of various diseases such as AIDS, avian influenza, cholera, Ebola, and Zika virus. Wang et al have investigated a virus infection model with density-dependent diffusion and Holling II type [6] or Beddington–DeAngelis type incidence function [7] subjected to the homogeneous Neumann boundary conditions. They have obtained the significant results of threshold dynamics and competitive exclusion. E rest of this paper is organized as follows: in Section 2, for the single-strain viral infection model (1), we shall prove the existence, uniqueness, and boundedness of solutions to problems (1)–(4) and consider the global threshold dynamics of the model through constructing appropriate Lyapunov functionals, which is determined by the reproductive numbers for viral infection R0.

Single-Strain Viral Infection Model

Multistrain Viral Infection Model

Space x 2

Numerical Calculations and Simulations

Conclusion