The impact of immune cell interactions on virus quasi-species formation

Ali Moussaoui; Vitaly Volpert; Ali Moussaoui; Vitaly Volpert

doi:10.3934/mbe.2024331

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 11: 7530-7553. doi: 10.3934/mbe.2024331

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The impact of immune cell interactions on virus quasi-species formation

Ali Moussaoui ^{1
,
,},
Vitaly Volpert ^2,3,4

1.
Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Department of Mathematics, Faculty of Science, University of Tlemcen, 13000, Algeria
2.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne 69622, France
3.
Peoples' Friendship University of Russia (RUDN University)
4.
Miklukho-Maklaya St, Moscow 117198, Russian Federation

Received: 27 July 2024 Revised: 18 October 2024 Accepted: 28 October 2024 Published: 11 November 2024

The process of viral infection spreading in tissues was influenced by various factors, including virus replication within host cells, transportation, and the immune response. Reaction-diffusion systems provided a suitable framework for examining this process. In this work, we studied a nonlocal reaction-diffusion system of equations that modeled the distribution of viruses based on their genotypes and their interaction with the immune response. It was shown that the infection may persist at a certain level alongside a chronic immune response, exhibiting spatially uniform or oscillatory behavior. Finally, the immune cells may become entirely depleted, leading to a high viral load persisting in the tissue. Numerical simulations were employed to elucidate the nonlinear dynamics and pattern formation inherent in the nonlocal model.
- virus density distribution,
- nonlocal interaction,
- genotype space,
- immune response,
- reaction-diffusion model
Citation: Ali Moussaoui, Vitaly Volpert. The impact of immune cell interactions on virus quasi-species formation[J]. Mathematical Biosciences and Engineering, 2024, 21(11): 7530-7553. doi: 10.3934/mbe.2024331

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Abstract

The process of viral infection spreading in tissues was influenced by various factors, including virus replication within host cells, transportation, and the immune response. Reaction-diffusion systems provided a suitable framework for examining this process. In this work, we studied a nonlocal reaction-diffusion system of equations that modeled the distribution of viruses based on their genotypes and their interaction with the immune response. It was shown that the infection may persist at a certain level alongside a chronic immune response, exhibiting spatially uniform or oscillatory behavior. Finally, the immune cells may become entirely depleted, leading to a high viral load persisting in the tissue. Numerical simulations were employed to elucidate the nonlinear dynamics and pattern formation inherent in the nonlocal model.

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