cell-to-cell

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

In this paper, we will study mathematically and numerically the dynamics of the hepatitis C virus disease with the consideration of two fundamental modes of transmission of the infection, namely virus-to-cell and cell-to-cell.  In our model, we will take into account the role of cure rate of the infected cells and the effect of the adaptive immunity.  The model consists of five nonlinear differential equations, describing the interaction between the uninfected cells, the infected cells, the hepatitis C virions and the adaptive immunity.  This immunity will be represented by the humoral and