Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal

• Published in: Nonlinear analysis: real world applications 2015-12, Vol.26, p.161-190
• Main Authors: Elaiw, A.M., AlShamrani, N.H.
• Format: Article
• Language: English
• Subjects: Activation; Asymptotic properties; Global stability; Humoral immune response; Lyapunov function; Mathematical analysis; Mathematical models; Nonlinear dynamics; Nonlinearity; Stability; Viral infection; Viruses
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2015.05.007

In this paper, we investigate the dynamical behavior of two nonlinear models for viral infection with humoral immune response. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The intrinsic growth rate of uninfected cells, incidence rate of infection, removal rate of infected cells, production rate of viruses, neutralization rate of viruses, activation rate of B cells and removal rate of B cells are given by more general nonlinear functions. The second model is a modification of the first one by including an eclipse stage of infected cells. We assume that 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 the all equilibria of the models. We perform some numerical simulations for the models with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.