Global Threshold Dynamics in Humoral Immunity Viral Infection Models Including an Eclipse Stage of Infected Cells

Abstract

ABSTRACT. In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

Modelling and analysis of a within-host model of hepatitis B and D co-infections

“…the humoral immune response is universal and necessary to eliminate or control the disease after viral infection [23]. Therefore, several mathematical models have been proposed to describe the virus dynamics with humoral immunity [24], [25], [26], [27], [28], [30], [31], [32]. Mostafa et al introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms [33].…”

Stability analysis of general viral infection models with humoral immunity

“…In reality, the humoral immune response is universal and necessary to eliminate or control the disease after viral infection [2]. Therefore, several mathematical models have been proposed to describe the virus dynamics with humoral immunity [7,8,10,28,30,34,35,37]. The basic virus dynamics model with humoral immune response has four state variables: x, the population of uninfected target cells; y, the population of productive infected cells; v, the population of free virus particles in the blood; and z, the population of B cells.…”