Modeling the Memory and Adaptive Immunity in Viral Infection

  • Adnane Boukhouima
  • Khalid Hattaf
  • Noura Yousfi


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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Adnane Boukhouima
    • 1
  • Khalid Hattaf
    • 1
    • 2
  • Noura Yousfi
    • 1
  1. 1.Laboratory of Analysis, Modeling and Simulation (LAMS)Faculty of Sciences Ben M’sik, Hassan II UniversityCasablancaMorocco
  2. 2.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)CasablancaMorocco

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