Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Salma M. Al-Tuwairqi; Sara K. Al-Harbi; Salma M. Al-Tuwairqi; Sara K. Al-Harbi

doi:10.3934/mbe.2022456

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 9792-9824. doi: 10.3934/mbe.2022456

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Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Academic Editor: Quentin Griette

Received: 20 May 2022 Revised: 16 June 2022 Accepted: 21 June 2022 Published: 08 July 2022

Saudi Arabia was among the countries that attempted to manage the COVID-19 pandemic by developing strategies to control the epidemic. Lockdown, social distancing and random diagnostic tests are among these strategies. In this study, we formulated a mathematical model to investigate the impact of employing random diagnostic tests to detect asymptomatic COVID-19 patients. The model has been examined qualitatively and numerically. Two equilibrium points were obtained: the COVID-19 free equilibrium and the COVID-19 endemic equilibrium. The local and global asymptotic stability of the equilibrium points depends on the control reproduction number $ \mathcal{R}_{c} $. The model was validated by employing the Saudi Ministry of Health COVID-19 dashboard data. Numerical simulations were conducted to substantiate the qualitative results. Further, sensitivity analysis was performed on $ \mathcal{R}_{c} $ to scrutinize the significant parameters for combating COVID-19. Finally, different scenarios for implementing random diagnostic tests were explored numerically along with the control strategies applied in Saudi Arabia.
- mathematical model,
- COVID-19,
- stability,
- random diagnoses,
- lockdown,
- social distancing,
- Saudi Arabia
Citation: Salma M. Al-Tuwairqi, Sara K. Al-Harbi. Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9792-9824. doi: 10.3934/mbe.2022456

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Abstract

Saudi Arabia was among the countries that attempted to manage the COVID-19 pandemic by developing strategies to control the epidemic. Lockdown, social distancing and random diagnostic tests are among these strategies. In this study, we formulated a mathematical model to investigate the impact of employing random diagnostic tests to detect asymptomatic COVID-19 patients. The model has been examined qualitatively and numerically. Two equilibrium points were obtained: the COVID-19 free equilibrium and the COVID-19 endemic equilibrium. The local and global asymptotic stability of the equilibrium points depends on the control reproduction number $ \mathcal{R}_{c} $. The model was validated by employing the Saudi Ministry of Health COVID-19 dashboard data. Numerical simulations were conducted to substantiate the qualitative results. Further, sensitivity analysis was performed on $ \mathcal{R}_{c} $ to scrutinize the significant parameters for combating COVID-19. Finally, different scenarios for implementing random diagnostic tests were explored numerically along with the control strategies applied in Saudi Arabia.

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