Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

Kaushik Dehingia; Anusmita Das; Evren Hincal; Kamyar Hosseini; Sayed M. El Din; Kaushik Dehingia; Anusmita Das; Evren Hincal; Kamyar Hosseini; Sayed M. El Din

doi:10.3934/mbe.2023887

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 20025-20049. doi: 10.3934/mbe.2023887

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Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

1.
Department of Mathematics, Sonari College, Sonari 785690, Assam, India
2.
Department of Mathematics, Near East University TRNC, Mersin 10, Turkey
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4.
Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

Received: 31 July 2023 Revised: 27 September 2023 Accepted: 24 October 2023 Published: 03 November 2023

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.
- mathematical modeling,
- SARS-CoV-2,
- time delay,
- stability,
- Hopf bifurcation,
- numerical simulations
Citation: Kaushik Dehingia, Anusmita Das, Evren Hincal, Kamyar Hosseini, Sayed M. El Din. Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 20025-20049. doi: 10.3934/mbe.2023887

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Abstract

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

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