Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response

A Non-Standard Finite Difference Scheme for a Diffusive HIV-1 Infection Model with Immune Response and Intracellular Delay

In this paper, we propose and study a diffusive HIV infection model with infected cells delay, virus mature delay, abstract function incidence rate and a virus diffusion term. By introducing the reproductive numbers for viral infection R0 and for CTL immune response number R1, we show that R0 and R1 act as threshold parameter for the existence and stability of equilibria. If R0≤1, the infection-free equilibrium E0 is globally asymptotically stable, and the viruses are cleared; if R1≤1<R0, the CTL-inactivated equilibrium E1 is globally asymptotically stable, and the infection becomes chronic but without persistent CTL response; if R1>1, the CTL-activated equilibrium E2 is globally asymptotically stable, and the infection is chronic with persistent CTL response. Next, we study the dynamic of the discreted system of our model by using non-standard finite difference scheme. We find that the global stability of the equilibria of the continuous model and the discrete model is not always consistent. That is, if R0≤1, or R1≤1<R0, the global stability of the two kinds model is consistent. However, if R1>1, the global stability of the two kinds model is not consistent. Finally, numerical simulations are carried out to illustrate the theoretical results and show the effects of diffusion factors on the time-delay virus model.

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles.