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A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

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In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely defined by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay affects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.


Bulletin of Mathematical Sciences and Applications (Volume 9)
B. El Boukari and N. Yousfi, "A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response", Bulletin of Mathematical Sciences and Applications, Vol. 9, pp. 53-68, 2014
Online since:
August 2014

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[1] N. Ali, G. Zaman, . Abdullah, A. Alqahtani, A. Alshomrani, "The Effects of Time Lag and Cure Rate on the Global Dynamics of HIV-1 Model", BioMed Research International, Vol. 2017, p. 1, 2017


[2] N. Akbari, R. Asheghi, M. Nasirian, "Stability and Dynamic of HIV-1 Mathematical Model with Logistic Target Cell Growth, Treatment Rate, Cure Rate and Cell-to-cell Spread", Taiwanese Journal of Mathematics, Vol. 26, 2022