Bifurcation analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions

TL;DR

This paper conducts a mathematical bifurcation analysis of an age-structured HIV infection model incorporating virus-to-cell and cell-to-cell transmissions, revealing conditions for periodic solutions and providing numerical validation.

Contribution

It introduces a novel age-structured HIV model with both transmission modes and analyzes its bifurcation behavior using advanced mathematical theories.

Findings

Existence of parameter values leading to periodic solutions

Bifurcation from the positive equilibrium

Numerical simulations support theoretical results

Abstract

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD4+ T cells by a logistic function and the infected CD4+ T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a non-trivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.