Modeling the Memory and Adaptive Immunity in Viral Infection

Adnane Boukhouima, Khalid Hattaf and Noura Yousfi
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Adnane Boukhouima: Faculty of Sciences Ben M’sik, Hassan II University, Laboratory of Analysis, Modeling and Simulation (LAMS)
Khalid Hattaf: Faculty of Sciences Ben M’sik, Hassan II University, Laboratory of Analysis, Modeling and Simulation (LAMS)
Noura Yousfi: Faculty of Sciences Ben M’sik, Hassan II University, Laboratory of Analysis, Modeling and Simulation (LAMS)

A chapter in Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics, 2019, pp 271-297 from Springer

Abstract: Abstract The adaptive immunity is a complex system that involves memory and plays an important role in the control of viral infection such as human immunodeficiency virus (HIV), hepatitis B virus (HBV), and hepatitis C virus (HCV). In this paper, we propose a mathematical model formulated by fractional differential equations in order to describe the role of the adaptive immunity in viral infections and take into account the memory effect. In the proposed model, the infection transmission is modeled by Hattaf–Yousfi functional response. We first show that the model is mathematically and biologically well-posed. Using appropriate Lyapunov functionals and LaSalle’s invariance principle, the global stability of the equilibria is established and characterized by five threshold parameters. Numerical simulations are presented to illustrate our theoretical results.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-23433-1_18

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DOI: 10.1007/978-3-030-23433-1_18

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