Stability analysis for delayed viral infection model with multitarget cells and general incidence rate

Abstract

In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected target cells, n classes of infected cells and nonlinear incidence rate h (x, v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model. Int. J. Biomath. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/19/15. For personal use only. Stability analysis for delayed viral infection model39], which lead mathematical models to delay differential equations. It is of interest from both mathematical and biological viewpoints to investigate whether Hopf bifurcations in in-host models are the result of target-cell dynamics, intracellular delays, or a combination of both. The result that intracellular delays will lead to period oscillations in in-host models only with the right kind of target-cell dynamics has been shown in Li et al. [17].Motivated by the studies of [12-15, 17, 19, 21], the main purpose of this paper is to give the conditions to ensure the permanence and complete global analysis of the 2n + 1-dimensional viral infection model. The model studied in this paper (compared to model (1.1)) include the following extensions:

Global properties of an age-structured virus model with saturated antibody immune response, multi-target cells and general incidence rate

“…In recent times, several mathematical models have been proposed in order to try to understand the mechanism of virus infections. These models often describe the changes through time in the concentration of infected and uninfected target cells and viral particles in the blood of an infected individual [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Modelling the effect of antibody immune response in the neutralization of virus is a very important topic for research since it can provide useful insights into the dynamics of the infection and offer suggestions for clinical treatment.…”

“…Therefore, we need to incorporate in our virus dynamic models a multi-group component to study virus infection in different populations of cells. Viral infection models dealing with the interaction of virus with more than one class of target cells have been studied in [7][8][9][10][11][12][13] and references cited therein.…”

“…However, there is certain debate that this rate is insufficient to realistically describe the infection process. Some authors have incorporated in their models several types of non-linear incidence functions, including saturated Holling type II incidence βT V /(1 + αV ) [3,5,15], Beddington-DeAngelis functional response βT V /(1 + aT + bV ) [6,7], or even more general functions, e.g., of the forms c(T )f (V ) [16] or h(T, V ) [4,8,9].…”