Analysis of an HTLV/HIV dual infection model with diffusion

A. M. Elaiw; N. H. AlShamrani; A. M. Elaiw; N. H. AlShamrani

doi:10.3934/mbe.2021464

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 9430-9473. doi: 10.3934/mbe.2021464

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Research article

Analysis of an HTLV/HIV dual infection model with diffusion

A. M. Elaiw ^1,2,
N. H. AlShamrani ^{1,3
,
,}

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71452, Egypt
3.
Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 10 August 2021 Accepted: 12 October 2021 Published: 28 October 2021

In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD$ 4^{+} $T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.
- HTLV/HIV dual infection,
- diffusion,
- global stability,
- mitosis,
- CTL immune response
Citation: A. M. Elaiw, N. H. AlShamrani. Analysis of an HTLV/HIV dual infection model with diffusion[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9430-9473. doi: 10.3934/mbe.2021464

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Abstract

In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD$ 4^{+} $T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.

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