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Modeling the Memory and Adaptive Immunity in Viral Infection

In: Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Author

Listed:
  • 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)
    Centre Régional des Métiers de l’Education et de la Formation (CRMEF))

  • Noura Yousfi

    (Faculty of Sciences Ben M’sik, Hassan II University, Laboratory of Analysis, Modeling and Simulation (LAMS))

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.

Suggested Citation

  • Adnane Boukhouima & Khalid Hattaf & Noura Yousfi, 2019. "Modeling the Memory and Adaptive Immunity in Viral Infection," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics, pages 271-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-23433-1_18
    DOI: 10.1007/978-3-030-23433-1_18
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