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: