| Summary: | The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious diseases, including forecasting outbreaks and designing containment strategies. In this paper, we study two types of SIR and SEIR models for the coronavirus. This study focuses on the discrete-time and fractional-order of these models; we study the stability of the fixed points and orbits using the Jacobian matrix and the eigenvalues and eigenvectors of each case; moreover, we estimate the parameters of the two systems in fractional order. We present a statistical study of the coronavirus model in two countries: Saudi Arabia, which has successfully recovered from the SARS-CoV-2 pandemic, and China, where the number of infections remains significantly high.
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