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

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 Rc. 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 Rc 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.