Mathematical Modeling and Analysis of COVID-19 Infection: Application to the Kingdom of Saudi Arabia Data

Abstract

To evaluate the probable effects of the COVID-19 outbreak on Saudi Arabia, a novel dynamical model is developed. Using the most recent instances of COVID-19 infection that have been reported in Saudi Arabia, we examine the roles of quarantine and hospitalization. The model’s mathematical outcomes are displayed. The model’s infection-free equilibrium is displayed, and asymptotically, it is determined to be both locally and globally stable. We demonstrate that the model is locally asymptotically stable (LAS) for the basic reproduction ${\mathcal{R}}_0<1$ . The model is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$ . To estimate the model parameters, recent COVID-19 instances in KSA that began between May 1, 2022, and August 4, 2022, are taken into account. We achieve the needed data fitting considering the approach of nonlinear least square, and we demonstrate that the predicted basic reproduction number is ${\mathcal{R}}_0\approx 1.2988$ . Graphical representations of the calculated parameters and their effects on disease eradication are provided. The findings show that the most effective way to reduce the number of new instances of infection is to limit the contact of exposed, asymptomatic, symptomatic, and hospitalized people with vulnerable. The percentage of exposed people who are quarantined also plays a big part in lowering the number of infected cases.