Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics
The authors suggest a multiscale model for the spread of the human immunodeficiency virus (HIV) in the population. Single-scale models have been used in the literature for describing either the within-host viral dynamics at the individual level (microscale) or the between-host virus transmission at the population level (macroscale). In this paper, both types of dynamics are biderectionally coupled and a multiscale model consisting of six differential equations is suggested for describing the dynamics of the virus spread. The macroscale variables include the number of susceptibles \(S,\) the number of HIV-positive individuals without clinical manifestation \(I,\) and the number of AIDS patients with the progressing infection \(A.\) The microscale variables \(T,\) \(T^{\ast},\) and \(V\) stand for the densities of healthy T-cells, infected T-cells and viral load respectively. The multiscale system combines the dynamics on a fast scale within a host and a slow-scale dynamics between hosts. Dynamics of the fast subsystem is studied first and the existence of the unique positive globally asymptotically stable equilibrium is established in Theorem 1. Then the analysis of the slow subsystem is conducted. A criterion for the local asymptotic stability of the disease-free equilibrium of the slow system in terms of the basic reproductive number \(R_{s}\) is given in Theorem 2. Theorem 3 provides conditions for the existence of positive equilibria for the slow subsystem and their number (no, one, or two equilibria). After this, local stability of the positive equilibrium is discussed. Numerical simulations are conducted to illustrate the occurrence of a backward bifurcation in the coupled system and the interplay between the slow and fast subsystems. The final section summarizes the main contributions made in the paper.
scientific article; zbMATH DE number 7390432
scientific article