The asymptotic stability of a fractional epidemiological model "Covid ۱۹ Variant Anglais" with Caputo derivative

We have all been injured by corona and its mutations, not just us but the whole world.  The global impact of coronavirus (COVID-۱۹) has been profound and the public health threat it represents is the most serious seen in a respiratory virus since ۱۹۱۸. This paper is concerned with a fractional order S_{N}S_{C}IR model involving the Caputo fractional derivative. The effective methods to solve the fractional epidemic models we introduced to construct a simple and effective analytical technique that can be easily extended and applied to other fractional models and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.  The equilibrium points and the basic reproduction number are computed. An analysis of the local asymptotic stability at the disease-free equilibrium is given; Next, we study the stability of the equilibrium points in the sense of Mittag-Leffler. Moreover, some numerical simulations are included to verify the theoretical achievement. These results provide good evidence for the implications of the theoretical results corresponding to the model.

Keywords:

Mittag-Leffler , Global Stability , Lyapunov function