Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy
Abstract
:1. Introduction
2. Derivation of the Mathematical Model
- : the uninfected susceptible target cells, which are surface epithelial cells with ACE-2 receptors located in the respiratory tract, including the lungs and nasal and trachea/ bronchial tissues;
- : the SARS-CoV-2-infected virus-producing cells;
- : the virus particles.
3. Dynamics of the Model without Impulses
3.1. Non-Negativity and Boundedness
3.2. Basic Reproduction Number
3.3. Existence of Equilibrium Points
3.4. Stability of Equilibrium Points
4. Dynamics of the System with Impulsive Drug Dosing
4.1. Dynamics of the Drug
4.1.1. Impact of Imperfect Drug Dosing
4.2. Dynamics of the Impulsive System (4)
5. Numerical Simulation
6. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
References
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Parameters | Short Description | Value (Unit) | References |
---|---|---|---|
Growth rate of epithelial cells | cells mL day | [48] | |
Natural death rate of uninfected epithelial cells | day | [11,48] | |
Blanket death rate of infected epithelial cells | day | [11] | |
Rate of infection | (5–561) mL (RNA copies) day | [24,31] | |
p | Growth rate of virus in cells | day | [48] |
Virus clearance rate | day | [24] | |
Rate of antibody response from immune cells | day | [48] | |
r | Viral particles’ rate of neutralization by antibodies | mL (molecules) day | [48] |
Half-maximal simulation threshold | (RNA copies) mL | [48] | |
Antibody clearance rate | day | [48] | |
Antibody production rate by drug | 6 molecules day gm | Assumed | |
Decay rate of drug | 0.1 mg day | Assumed |
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Chatterjee, A.N.; Basir, F.A.; Biswas, D.; Abraha, T. Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy. Vaccines 2022, 10, 1846. https://doi.org/10.3390/vaccines10111846
Chatterjee AN, Basir FA, Biswas D, Abraha T. Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy. Vaccines. 2022; 10(11):1846. https://doi.org/10.3390/vaccines10111846
Chicago/Turabian StyleChatterjee, Amar Nath, Fahad Al Basir, Dibyendu Biswas, and Teklebirhan Abraha. 2022. "Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy" Vaccines 10, no. 11: 1846. https://doi.org/10.3390/vaccines10111846
APA StyleChatterjee, A. N., Basir, F. A., Biswas, D., & Abraha, T. (2022). Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy. Vaccines, 10(11), 1846. https://doi.org/10.3390/vaccines10111846