In this article, we study the global stability of fractional partial differential equations applied to the biological system modeling a viral infection. The reaction in the proposed biological system is described by the new generalized Hattaf fractional (GHF) derivative. However, the diffusion is modeled by the Laplacian operator.
This paper aims to prezent mathematical model for Viral infection which incorporates both the cell-free and cell-to-cell transmission. The model includes four compartments, namely, the susceptible, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus. Firstly, we establish the well-posedness of our mathematical model in terms of proving the existence, positivity and boundedness of solutions. Moreover, we determine the different equilibrium of the problem. Also, we will study the global stability of each equilibrium. Final
Fractional HCV infection model with adaptive immunity and treatment is suggested and studied in this paper. The adaptive immunity includes the CTL response and antibodies. This model contains five ordinary differential equations. We will start our study by proving the existence, uniqueness, and boundedness of the positive solutions. The model has free-equilibrium points and other endemic equilibria. By using Lyapunov functional and LaSalle's invariance principle, we have shown the global stability of these equilibrium points. Finally, some numerical simulations will be given to valid
The global analysis of a spatio-temporal fractional order SEIR infection epidemic model is studied and analyzed in this paper. The dynamics of the infection is described by four partial differential equations with a fractional derivative order and with diffusion. The equations of our model describe the evolution of the susceptible, the exposed, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment. At first, we will prove the existence and uniqueness of the solution using the results of the fixed point theorem