(untitled) (Journal of Engineering, 2025)
Whenever a mathematical model is suggested to classing COVID-19. The population must be divided into several groups and our model has five groups namely S(t), E(t), I(t), V(t) and R(t) which represent susceptible, exposed, inflected, vaccinated and recovered individuals respectively. This model is a continuous dynamical system where the derivative is in fractional form. An analysis solution evaluates the positivity of the functions S(t), E(t), I(t), V(t) and R(t) as solutions of the system. The uniformity of the solutions of the system under consideration is also proved. And finding the equilibrium points. To get acceptable results one needs the solutions. Some of the solutions are points called equilibrium points and the other are functions. and studying their stability fractional differential system orders are checked locally and globally. The basic reproduction number is used to prove the stability of all equilibrium points as well as the method of the nature of the eigenvalues of the Jacobian at each equilibrium point. And then studied the local bifurcation to the asymptotically stable and stable equilibrium points. And evaluated approximately. These solutions must satisfy the nature of the problem under consideration for example under certain conditions some of the equilibrium points are stable. Also, the approximate solution must give results close to the real situation. All these demands are shown in this paper. Approximate and Numerical simulation is given through a tables and graphs which shows the efficiency of the method, using the MATLAP to all the figures.