The influence of immune cells on the existence of virus quasi-species

Ali Moussaoui; Vitaly Volpert; Ali Moussaoui; Vitaly Volpert

doi:10.3934/mbe.2023710

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 15942-15961. doi: 10.3934/mbe.2023710

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The influence of immune cells on the existence of virus quasi-species

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

1.
Laboratoire d'Analyse Non linéaire et Mathématiques Appliquées, Department of Mathematics, Faculty of Sciences, University of Tlemcen, Algeria
2.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne 69622, France
3.
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation

Academic Editor: Jia Li

Received: 30 March 2023 Revised: 07 July 2023 Accepted: 23 July 2023 Published: 02 August 2023

This article investigate a nonlocal reaction-diffusion system of equations modeling virus distribution with respect to their genotypes in the interaction with the immune response. This study demonstrates the existence of pulse solutions corresponding to virus quasi-species. The proof is based on the Leray-Schauder method, which relies on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions. Furthermore, linear stability analysis of a spatially homogeneous stationary solution identifies the critical conditions for the emergence of spatial and spatiotemporal structures. Finally, numerical simulations are used to illustrate nonlinear dynamics and pattern formation in the nonlocal model.
- virus density distribution,
- nonlocal interaction,
- genotype space,
- immune response,
- reaction-diffusion model
Citation: Ali Moussaoui, Vitaly Volpert. The influence of immune cells on the existence of virus quasi-species[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 15942-15961. doi: 10.3934/mbe.2023710

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Abstract

This article investigate a nonlocal reaction-diffusion system of equations modeling virus distribution with respect to their genotypes in the interaction with the immune response. This study demonstrates the existence of pulse solutions corresponding to virus quasi-species. The proof is based on the Leray-Schauder method, which relies on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions. Furthermore, linear stability analysis of a spatially homogeneous stationary solution identifies the critical conditions for the emergence of spatial and spatiotemporal structures. Finally, numerical simulations are used to illustrate nonlinear dynamics and pattern formation in the nonlocal model.

References

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