Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response

Khalid Hattaf; Noura Yousfi; Khalid Hattaf; Noura Yousfi

doi:10.3934/mbe.2020288

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5326-5340. doi: 10.3934/mbe.2020288

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Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response

Khalid Hattaf ^{1,2
,
,},
Noura Yousfi ²

1.
Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco
2.
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco

Received: 18 June 2020 Accepted: 05 August 2020 Published: 12 August 2020

In this paper, we propose a new within-host model which describes the interactions between SARS-CoV-2, host pulmonary epithelial cells and cytotoxic T lymphocyte (CTL) cells. Furthermore, the proposed model takes into account the lytic and nonlytic immune responses and also incorporates both modes of transmission that are the virus-to-cell infection through extracellular environment and the cell-to-cell transmission via virological synapses. The well-posedness of the model as well as the existence of equilibria are established rigorously. Moreover, the dynamical behaviour of the model is further examined by two threshold parameters, and the biological aspects of the analytical results are further presented.
- COVID-19,
- SARS-CoV-2,
- lytic and nonlytic immune responses,
- mathematical modeling,
- stability analysis
Citation: Khalid Hattaf, Noura Yousfi. Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5326-5340. doi: 10.3934/mbe.2020288

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Abstract

In this paper, we propose a new within-host model which describes the interactions between SARS-CoV-2, host pulmonary epithelial cells and cytotoxic T lymphocyte (CTL) cells. Furthermore, the proposed model takes into account the lytic and nonlytic immune responses and also incorporates both modes of transmission that are the virus-to-cell infection through extracellular environment and the cell-to-cell transmission via virological synapses. The well-posedness of the model as well as the existence of equilibria are established rigorously. Moreover, the dynamical behaviour of the model is further examined by two threshold parameters, and the biological aspects of the analytical results are further presented.

References

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