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Analysis of an age-structured HIV in-host model with proliferation and two infection modes

Part of: General first-order equations and systems Stability theory

Published online by Cambridge University Press:  08 October 2019

DONGXUE YAN ,
XIANLONG FU  and
XINGFU ZOU Open the ORCID record for XINGFU ZOU [Opens in a new window]
DONGXUE YAN
Affiliation:
Department of Information and Computation Sciences, School of Science, Nanjing University of Posts and TelecommunicationsNanjing210023, P. R. China
XIANLONG FU
Affiliation:
Department of Applied Mathematics, School of Mathematical Sciences & Shanghai Key Laboratory of PMMP East China Normal University, Shanghai200241, P. R. China
XINGFU ZOU
Affiliation:
Department of Applied Mathematics, University of Western Ontario London, Ontario N6A 5B7, Canada email: xzou@uwo.ca
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Abstract

We propose and analyse an age-structured model for within-host HIV virus dynamics which is incorporated with both virus-to-cell and cell-to-cell infection routes, and proliferations of both uninfected and infected cells in the form of logistic growth. The model turns out to be a hybrid system with two differential-integral equations and one first-order partial differential equation. We perform some rigorous analyses for the considered model. Among the interesting dynamical behaviours of the model is the occurrence of backward bifurcation in terms of the basic reproduction number R0 at R0 = 1, which raises new challenges for effective infection control. We also discuss the cause of such a backward bifurcation, based on our analytical results.

Keywords

HIV in-host modelinfection ageproliferationstabilitybackward bifurcation

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 34D20: Stability 35F30: Boundary value problems for nonlinear first-order equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 5 , October 2020 , pp. 806 - 827
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Copyright
© Cambridge University Press 2019

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Footnotes

†

Research partially supported by China Scholarship Council, NSF of China (Nos. 11671142 and 11771075) and NSERC of Canada (No. RGPIN-2016-04665).

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