Stability analysis of general viral infection models with humoral immunity

Abstract

We present two nonlinear viral infection models with humoral immune response and investigate their global stability. The first model describes the interaction of the virus, uninfected cells, infected cells and B cells. This model is an improvement of some existing models by incorporating more general nonlinear functions for: (i) the intrinsic growth rate of uninfected cells; (ii) the incidence rate of infection; (iii) the removal rate of infected cells; (iv) the production, death and neutralize rates of viruses; (v) the activation and removal rate of B cells. In the second model, we introduce an additional population representing the latently infected cells. The latent-to-active conversion rate is also given by a more general nonlinear function. For each model, we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle's invariance principle, we prove the global asymptotic stability of all equilibria of the models.

Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

“…In the virus dynamics literature, several mathematical models have incorporated CTL immune response 2-5 and humoral immune response. [6][7][8][9][10][11] Intracellular time delay discrete or distributed has also been considered in the mathematical models of virus dynamics in several works (see e.g., Refs. 13 and 12-18.…”

“…It is observed that, no HIV infection model with this type of infected-to-target infection has considered the effect of immune response. Humoral immunity has been incorporated into virus dynamics models in several works, [6][7][8][9][10][11] however, in these papers, only virus-to-cell transmission has been considered. Therefore, reasonable mathematical models for HIV-1 with virus-to-target and infected-to-target infections should take humoral immunity into consideration.…”

Dynamics of a nonlocal dispersal in‐host viral model with humoral immunity

“…System (1) is the basis of many studies. For instance, based on system (1), Elaiw and Shamrani 11 formulated two nonlinear viral infection models with humoral immune response by considering more general nonlinear functions for the incidence, production, and removal rates, and investigated their global stability. Incorporated two distributed intracellular delays and one discrete immunological delay, Hattaf 12 established a generalized viral infection model with multidelays and humoral immunity and formulated the global stability and Hopf bifurcation of the model.…”