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Bulletin of mathematical biology
01 16, 2021;83 (3): 18.

A Network Immuno-Epidemiological HIV Model.

Churni Gupta, Necibe Tuncer, Maia Martcheva
Author Information
  1. Churni Gupta: Department of Mathematics, University of Florida, Gainesville, USA. churnibidisha@ufl.edu. ORCID
  2. Necibe Tuncer: Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, USA. ntuncer@fau.edu.
  3. Maia Martcheva: Department of Mathematics, University of Florida, Gainesville, USA. maia@ufl.edu.
PMID: 33452941 DOI: 10.1007/s11538-020-00855-3

Abstract

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number [Formula: see text] of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when [Formula: see text] and unstable when [Formula: see text]. Numerical simulations suggest that [Formula: see text] increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes.

Keywords

Age structured Basic reproduction number Epidemic model HIV Network

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MeSH Term

HIV Infections
Humans
Mathematical Concepts
Models, Biological
Journal Article Research Support, U.S. Gov't, Non-P.H.S.
Article has an altmetric score of 5

Word Cloud

Created with Highcharts 10.0.0modelnumber[Formula:seetext]equilibriumHIVreproductionnodesnetworkmulti-scaleimmuno-epidemiologicalsystemdifferentialdisease-freeincreasesconnectivityNetworkpaperformulatenestedcomplexnetworksdescribedordinaryequationscoupledpartialequationFirstproveexistenceuniquenessimmunologicalestablishwell-posednessderiveexplicitexpressionbasicendemicgloballystableunstableNumericalsimulationssuggestfindscale-freeinfectedindividualshump-likefunctionwithin-hosthoweverdependencebecomesmonotonepredominantlylowhighImmuno-EpidemiologicalModelAgestructuredBasicEpidemic

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