Abstract
In this work, we study a mathematical model describing the human immunodeficiency virus (HIV) with the adaptive immune response, three saturated rates and therapy. The considered adaptive immunity is constituted by cytotoxic T-lymphocytes (CTL) immune cells and antibodies; the three saturated rates describe the viral infection, the CTLs and the antibodies proliferations. Two types of treatments are integrated into the model; the objective of the first one is to reduce the infected cells number, however the role of the second is to obstruct the free viruses expansion. The positivity and boundedness of solutions are proved. The local stability of the disease free steady state and the infection steady states is studied. Numerical simulations are performed in order to show the behavior of solutions, the effect of the antibodies proliferation saturated rate and the effectiveness of the incorporated therapies in controlling HIV replication.
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Acknowledgements
Karam Allali thanks to the International Union of Biological Sciences (IUBS) for partial support of living expenses in Moscow, during the 17th BIOMAT International Symposium, October 29–November 04, 2017.
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Allali, K. (2018). Modelling the Adaptive Immune Response in HIV Infection with Three Saturated Rates and Therapy. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_18
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