Mathematical modelling of COVID-19 disease dynamics: Interaction between immune system and SARS-CoV-2 within host

S. M. E. K. Chowdhury; J. T. Chowdhury; Shams Forruque Ahmed; Praveen Agarwal; Irfan Anjum Badruddin; Sarfaraz Kamangar; S. M. E. K. Chowdhury; J. T. Chowdhury; Shams Forruque Ahmed; Praveen Agarwal; Irfan Anjum Badruddin; Sarfaraz Kamangar

doi:10.3934/math.2022147

AIMS Mathematics

2022, Volume 7, Issue 2: 2618-2633. doi: 10.3934/math.2022147

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Mathematical modelling of COVID-19 disease dynamics: Interaction between immune system and SARS-CoV-2 within host

1.
Department of Mathematics, University of Chittagong, Chattogram 4331, Bangladesh
2.
Science and Math Program, Asian University for Women, Chattogram 4000, Bangladesh
3.
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
4.
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman AE 346, United Arab Emirates
5.
International Center for Basic and Applied Sciences, Jaipur 302029, India
6.
Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia

Received: 23 September 2021 Accepted: 05 November 2021 Published: 17 November 2021
MSC : 34A12, 34A34, 37C75

SARS-COV-2 (Coronavirus) viral growth kinetics within-host become a key fact to understand the COVID-19 disease progression and disease severity since the year 2020. Quantitative analysis of the viral dynamics has not yet been able to provide sufficient information on the disease severity in the host. The SARS-CoV-2 dynamics are therefore important to study in the context of immune surveillance by developing a mathematical model. This paper aims to develop such a mathematical model to analyse the interaction between the immune system and SARS-CoV-2 within the host. The model is developed to explore the viral load dynamics within the host by considering the role of natural killer cells and T-cell. Through analytical simplifications, the model is found well-posed and asymptotically stable at disease-free equilibrium. The numerical results demonstrate that the influx of external natural killer (NK) cells alone or integrating with anti-viral therapy plays a vital role in suppressing the SARS-CoV-2 growth within-host. Also, within the host, the virus can not grow if the virus replication rate is below a threshold limit. The developed model will contribute to understanding the disease dynamics and help to establish various potential treatment strategies against COVID-19.
- MERS-CoV,
- SARS-CoV-2,
- COVID-19,
- mathematical model,
- immune system,
- basic reproduction number
Citation: S. M. E. K. Chowdhury, J. T. Chowdhury, Shams Forruque Ahmed, Praveen Agarwal, Irfan Anjum Badruddin, Sarfaraz Kamangar. Mathematical modelling of COVID-19 disease dynamics: Interaction between immune system and SARS-CoV-2 within host[J]. AIMS Mathematics, 2022, 7(2): 2618-2633. doi: 10.3934/math.2022147

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Abstract

SARS-COV-2 (Coronavirus) viral growth kinetics within-host become a key fact to understand the COVID-19 disease progression and disease severity since the year 2020. Quantitative analysis of the viral dynamics has not yet been able to provide sufficient information on the disease severity in the host. The SARS-CoV-2 dynamics are therefore important to study in the context of immune surveillance by developing a mathematical model. This paper aims to develop such a mathematical model to analyse the interaction between the immune system and SARS-CoV-2 within the host. The model is developed to explore the viral load dynamics within the host by considering the role of natural killer cells and T-cell. Through analytical simplifications, the model is found well-posed and asymptotically stable at disease-free equilibrium. The numerical results demonstrate that the influx of external natural killer (NK) cells alone or integrating with anti-viral therapy plays a vital role in suppressing the SARS-CoV-2 growth within-host. Also, within the host, the virus can not grow if the virus replication rate is below a threshold limit. The developed model will contribute to understanding the disease dynamics and help to establish various potential treatment strategies against COVID-19.

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