Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation

Mehdi Maziane, Khalid Hattaf and Noura Yousfi

International Journal of Differential Equations, 2018, vol. 2018, 1-9

Abstract:

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.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJDE/2018/3294268.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJDE/2018/3294268.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:3294268

DOI: 10.1155/2018/3294268

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().