Abstract
We propose an epidemic model as a system of FDEs to describe transmission amongst different locations that affect the epidemiological spread and the vaccination to control the disease. Our primary target is to focus on the necessity of the lockdown period, sometimes seen as interfering with private life in mobility, and the need for vaccines to minimize the transmission in the interior and external stages. We prove that controlling social contact was necessary during the pandemic spread to stop transmissions between different locations (travel, periodic lockdowns, social distance,…) and that re-vaccinations were needed to avoid reinfections.Using Routh Hurwitz's theory, we examin the local stability of the equilibrium points—the disease-free and coexisting. Employing the Lyapunov function, our research demonstrate global asymptotic stability towards the equilibrium points. At the end of the study, we provide some numerical simulations to corroborate our theoretical findings.
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