Dynamics of a nonlinear infection viral propagation model with one fixed boundary and one free boundary

TL;DR

This paper analyzes a nonlinear viral infection model with diffusion, fixed and free boundaries, showing habitat expansion, virus extinction when R0 ≤ 1, and persistence when R0 > 1, based on equilibrium solutions.

Contribution

It introduces a novel analysis of a viral propagation model with a free boundary, focusing on existence and uniqueness of equilibrium solutions for different R0 values.

Findings

Habitat always expands to [0, ∞)

Virus and infected cells die out if R0 ≤ 1

Virus persists when R0 > 1

Abstract

In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always expands to the half line $[0, \infty)$, and that the virus and infected cells always die out when the {\it Basic Reproduction Number} $\mathcal{R}_0\le 1$, while the virus and infected cells have persistence properties when $\mathcal{R}_0>1$. To obtain the persistence properties of virus and infected cells when $\mathcal{R}_0>1$, the most work of this paper focuses on the existence and uniqueness of positive equilibrium solutions for subsystems and the existence of positive equilibrium solutions for the entire system.