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Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation
Joint Authors
Yousfi, Noura
Maziane, Mehdi
Hattaf, Khalid
Source
International Journal of Differential Equations
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-01
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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 R0 and the CTL immune response reproduction number R1.
The stability of the last equilibrium depends on R0 and R1 as well as time delay τ 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 τ passes through a certain critical value.
American Psychological Association (APA)
Maziane, Mehdi& Hattaf, Khalid& Yousfi, Noura. 2018. Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation. International Journal of Differential Equations،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1170760
Modern Language Association (MLA)
Maziane, Mehdi…[et al.]. Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation. International Journal of Differential Equations No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1170760
American Medical Association (AMA)
Maziane, Mehdi& Hattaf, Khalid& Yousfi, Noura. Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation. International Journal of Differential Equations. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1170760
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1170760