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

Abstract

<abstract><p>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.</p></abstract>