A mathematical model for the spread of COVID-19 and control mechanisms in Saudi Arabia

In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease (COVID-19) in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk S_L and high-risk S_M susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals I_U and the one consisting of infected diagnosed individuals I_D); the compartment of recovered undiagnosed individuals R_U, that of recovered diagnosed R_D individuals, and the compartment of extinct Ex individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. We perform a parameter estimation over a short period of the total duration of the pandemic based on the COVID-19 epidemiological data, including the number of infected, recovered, and extinct individuals, in different time episodes of the COVID-19 spread.