Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics
type: Item
instance of: scholarly article
title: Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics
zbMATH Open document ID: 1485.92170
author: Yuyi Xue
author: Yanni Xiao
published in: Mathematical Biosciences and Engineering
publication date: 2021-09-03T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37G10
zbMATH DE Number: 7390432
zbMATH Keywords: mathematical model
zbMATH Keywords: human immunodeficiency virus
zbMATH Keywords: equilibria
zbMATH Keywords: stability
zbMATH Keywords: backward bifurcation
reviewed by: Yuriy V. Rogovchenko
Wikidata QID: Q104619340
MaRDI profile type: Publication
full work available at URL: mbe.2020350
OpenAlex ID: W3089475885
cites work: Q4255467
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DOI: 10.3934/MBE.2020350
description: scientific article; zbMATH DE number 7390432