Summary

In this study, we investigate the COVID-19 biological model, which was developed using data from Wuhan, Portugal, and Spain. The ordinary differential model and fractional differential model are separetely studied. The purpose of first part is to investigate the model’s stability using different approaches. The second is devoted to demonstrate the existence and uniqueness problem of solutions of the fractional part of the model.

The Lyapunov direct method and anther approaches are used to examine the stability of the given model. Then, since the system has one equilibrium point and this point contains a free variable, we perturb the system by introducing the small parameters  , where . Two equilibrium points are found after the system has been perturbed, and the Lyapunov direct approach (using the Routh-Hwartiz method and the Gershgorin theorem) is then used to show that the system is stable throughout the entire neighborhood.

Finally, the focus has been on the fractional differential model to show that a solution exists and then is unique for the considered model.