International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2018 (2018), Article ID 3294268, 9 pages.
Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation
We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number and the CTL immune response reproduction number . The stability of the last equilibrium depends on and as well as time delay in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when passes through a certain critical value.
Int. J. Differ. Equ., Volume 2018 (2018), Article ID 3294268, 9 pages.
Received: 20 August 2017
Accepted: 31 January 2018
First available in Project Euclid: 12 April 2018
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Maziane, Mehdi; Hattaf, Khalid; Yousfi, Noura. Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation. Int. J. Differ. Equ. 2018 (2018), Article ID 3294268, 9 pages. doi:10.1155/2018/3294268. https://projecteuclid.org/euclid.ijde/1523498446