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A compressive mathematical model including an eclipse stage of infected cells to study the impact of stem cells transplantation on one HIV1 patient

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A Correction to this article was published on 21 February 2022

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Abstract

We propose a new mathematical model to study the effect of stem cells transplantation on HIV-1 patient as a system of first order nonlinear ordinary differential equations. We include in this model five populations: stem cells, free virus, productively infected cells, infected cells in the eclipse stage and non-infected T cells. The model admits two equilibrium states: a non-infected point and an endemically infected one. The study of the stability of the system before treatment is already known: If the “basic reproduction number” is smaller than 1, then the free disease point is asymptotically stable. If the “basic reproduction number” is greater than 1, then the endemic point is asymptotically stable. The study of the stability of the system after treatment proves that, for a patient with an initial “basic reproduction number”, greater than 1, if it is possible for the therapy to lower this ratio under 1, then the patient will recover. If it is not possible to lower the ratio under 1, the HIV infection persists, but, it is possible to offer to the patient a better life.

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Acknowledgements

This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program.

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Authors and Affiliations

  1. LR03ES04, Faculté des Sciences de Tunis, Université de Tunis el Manar, 2092, Tunis, Tunisia

    Saoussan Kallel-Jallouli

  2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

    Sundus Naji Alaziz

Authors
  1. Saoussan Kallel-Jallouli
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  2. Sundus Naji Alaziz
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Contributions

Formulation of a new mathematical model that describes the impact of stem cell transplantation in HIV 1 patient. Then, we study the stability to conclude on the efficacy of the therapy.

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Correspondence to Sundus Naji Alaziz.

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The authors declared that they have no conflict of interest.

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Kallel-Jallouli, S., Alaziz, S.N. A compressive mathematical model including an eclipse stage of infected cells to study the impact of stem cells transplantation on one HIV1 patient. Netw Model Anal Health Inform Bioinforma 10, 9 (2021). https://doi.org/10.1007/s13721-020-00282-3

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  • DOI: https://doi.org/10.1007/s13721-020-00282-3

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