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 SL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{L}$\end{document} and high-risk SM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{M}$\end{document} susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals IU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{U}$\end{document} and the one consisting of infected diagnosed individuals ID\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{D}$\end{document}); the compartment of recovered undiagnosed individuals RU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{U}$\end{document}, that of recovered diagnosed RD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{D}$\end{document} 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.