Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Bibi Fatima; Mehmet Yavuz; Mati ur Rahman; Fuad S. Al-Duais; Bibi Fatima; Mehmet Yavuz; Mati ur Rahman; Fuad S. Al-Duais

doi:10.3934/mbe.2023527

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11847-11874. doi: 10.3934/mbe.2023527

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Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

1.
Department of Mathematics, University of Malakand, Chakadara Dir (Lower), 18800, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Türkiye
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4.
Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Aflaj 11942, Saudi Arabia
5.
Administration Department, Administrative Science College, Thamar University, Thamar, Yemen

Academic Editor: Yang Kuang

Received: 23 December 2022 Revised: 04 April 2023 Accepted: 22 April 2023 Published: 09 May 2023

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.
- epidemic model,
- MERS-CoV,
- next generation matrix technique,
- stability analysis,
- sensitivity analysis,
- optimal control,
- numerical simulations
Citation: Bibi Fatima, Mehmet Yavuz, Mati ur Rahman, Fuad S. Al-Duais. Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11847-11874. doi: 10.3934/mbe.2023527

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Abstract

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

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