Research Article | | Peer-Reviewed

### Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis

Received: 12 March 2024    Accepted: 7 April 2024    Published: 9 May 2024
Abstract

Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to R0. Finally, the numerical results with Matlab are in conformity with theoretical results.

 Published in International Journal of Systems Science and Applied Mathematics (Volume 9, Issue 1) DOI 10.11648/j.ijssam.20240901.12 Page(s) 9-19 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2024. Published by Science Publishing Group
Keywords

COVID-19, Chronic Disease, Mathematical Model, Stability, Sensitivity Analysis, Numerical Simulation

References
• APA Style

Somé, W., Kaboré, G., Lamien, K., Diallo, I., So, O., et al. (2024). Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis. International Journal of Systems Science and Applied Mathematics, 9(1), 9-19. https://doi.org/10.11648/j.ijssam.20240901.12

ACS Style

Somé, W.; Kaboré, G.; Lamien, K.; Diallo, I.; So, O., et al. Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis. Int. J. Syst. Sci. Appl. Math. 2024, 9(1), 9-19. doi: 10.11648/j.ijssam.20240901.12

AMA Style

Somé W, Kaboré G, Lamien K, Diallo I, So O, et al. Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis. Int J Syst Sci Appl Math. 2024;9(1):9-19. doi: 10.11648/j.ijssam.20240901.12

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author = {Windjiré Somé and Germain Kaboré and Kassiénou Lamien and Ismaël Diallo and Ousséni So and Blaise Somé},
title = {Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis},
journal = {International Journal of Systems Science and Applied Mathematics},
volume = {9},
number = {1},
pages = {9-19},
doi = {10.11648/j.ijssam.20240901.12},
url = {https://doi.org/10.11648/j.ijssam.20240901.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20240901.12},
abstract = {Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to R0. Finally, the numerical results with Matlab are in conformity with theoretical results.},
year = {2024}
}
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JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
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SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20240901.12
AB  - Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to R0. Finally, the numerical results with Matlab are in conformity with theoretical results.
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Author Information
• Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

• Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

• Department of Mathematics, Ecole Normale Supérieure, Koudougou, Burkina Faso

• Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso;Departement of Health , Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

• Department of Mathematics, Ecole Normale Supérieure, Koudougou, Burkina Faso

• Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

• Sections