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

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

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: [email protected]
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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).

References

Briton, N. F. (2003) Essential Mathematical Biology, Springer-Verlag, London.CrossRefGoogle Scholar
Browne, C. J. & Pilyugin, S. S. (2013) Global analysis of age-structured within-host virus model. Discrete Contin. Dyn. Syst. Ser. B 18, 1999–2017.Google Scholar
Culshaw, R. V., Ruan, S. & Webb, G. (2003) A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46, 425–444.CrossRefGoogle ScholarPubMed
Dai, L. & Zou, X. (2015) Analysis of a within-host age-structured model with mutations between two viral strains. J. Math. Anal. Appl. 426, 953–970.CrossRefGoogle Scholar
De Leenheer, P. & Smith, H. L. (2003) Virus dynamics: a global analysis. SIAM J. Appl. Math. 63, 1313–1327.Google Scholar
Engel, K. J. & Nagel, R. (2000) One-Parameter Semigroups for Linear Evolution Equations, Springer, New York.Google Scholar
Gomez-Acevedo, H. & Li, M. Y. (2005) Backward bifurcation in a model for HTLV-I infection of CD4 T cells. Bull. Math. Biol. 67, 101–114.CrossRefGoogle Scholar
Gummuluru, S., Kinsey, C. M. & Emerman, M. (2000) An in vitro rapid-turnover assay for human immunodeficiency virus type 1 replication selects for cell-to-cell spread of virua. J. Virol. 74, 10882–10891.CrossRefGoogle Scholar
Kot, M. (2001) Elements of Mathematical Ecology, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Lai, X. & Zou, X. (2014) Dynamics of evolutionary competition between budding and lytic viral release strategies. Math. Biol. Eng. 11, 1091–1113.Google ScholarPubMed
Lai, X. & Zou, X. (2014) Modeling HIV-1 virus dynamicswith both virus-to-cell infection and cell-to-cell transmission. SIAM J. Appl. Math.. 74, 898–917.CrossRefGoogle Scholar
Lai, X. & Zou, X. (2015) Modeling cell-to-cell spread of HIV-1 with logistic target cell growth. J. Math. Anal. Appl. 426, 563–584.CrossRefGoogle Scholar
Li, M. Y. & Wang, L. C. (2014) Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment. Nonlinear Anal. Real World Appl. 17, 147–160.CrossRefGoogle Scholar
Nelson, P. W., Gilchrist, M. A., Coombs, D., Hyman, J. M. & Perelson, A. S. (2004) An agestructured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Math. Biosci. Eng. 1, 267–288.CrossRefGoogle ScholarPubMed
Nowak, M. A. & May, R. M. (2000) Virus Dynamics: Mathematical Principle of Immunology and Virology, Oxford University Press, New York.Google Scholar
Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York.CrossRefGoogle Scholar
Perelson, A. S. & Nelson, P. W. (1999) Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3–44.CrossRefGoogle Scholar
Philips, D. M. (1994) The role of cell-to-cell transmission in HIV infection. AIDS 8, 719–731.CrossRefGoogle Scholar
Qesmi, R., Elsaadany, S., Heffernan, J. M. & Wu, J. (2011) A hepatitis B and C virus model with age since infection that exhibits backward bifurcation. SIAM J. Appl. Math. 71, 1509–1530.CrossRefGoogle Scholar
Rong, L., Feng, Z. & Perelson, A. S. (2007) Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy. SIAM J. Appl. Math. 67, 731–756.CrossRefGoogle Scholar
Sato, H., Orenstein, J., Dimitrov, D. S. & Martin, M. A. (1992) Cell-to-cell spread of HIV-1 occurs with minutes and may not involve the participation of virus particles. Virology 186, 712–724.CrossRefGoogle Scholar
Thieme, H. R. & Castillo-Chavez, C. (1993) How may the infection-age-dependent infectivity affect the dynamics of HIV/AIDS. SIAM J. Appl. Math. 53, 1447–1479.CrossRefGoogle Scholar
Wang, L. & Ellermeyer, S. (2006) HIV infection and CD4+ T cell dynamics. Discrete Contin. Dyn. Syst. Ser. B 6, 1417–1430.Google Scholar
Wang, J., Lang, J. & Zou, X. (2017) Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission. Nonl. Anal. (RWA) 34, 75–96.CrossRefGoogle Scholar
Wang, L. & Li, M.Y. (2006) Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. Math. Biosci. 200, 44–57.CrossRefGoogle Scholar
Wang, Y., Liu, K. & Lou, Y. (2017) An age-structured within-host HIV model with T-cell competition. Nonl. Analy. Real World Appl. 38, 1–20.CrossRefGoogle Scholar