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  4. Fractional HCV infection model with adaptive immunity and treatment

Fractional HCV infection model with adaptive immunity and treatment

MMC.
2023;
Volume 10, Number 4
: pp. 995–1013
https://doi.org/10.23939/mmc2023.04.995
Received: June 01, 2023
Revised: September 24, 2023
Accepted: October 03, 2023

Mathematical Modeling and Computing, Vol. 10, No. 4, pp. 995–1013 (2023)

Authors:
  1. Z. Yaagoub
  2. K. Allali
1
Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca
2
Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca

Fractional HCV infection model with adaptive immunity and treatment is  suggested and studied in this paper.  The adaptive immunity includes the CTL response and antibodies.  This model contains five ordinary differential equations.  We will start our study by proving the existence, uniqueness, and boundedness of the positive solutions.  The model has free-equilibrium points and other endemic equilibria.  By using Lyapunov functional and LaSalle's invariance principle, we have shown the global stability of these equilibrium points.  Finally, some numerical simulations will be given to validate our theoretical results and show the effect of the fractional derivative order parameter and the other treatment parameters.

fractional order
HCV
cell-to-cell
virus-to-cell
global stability
numerical simulations
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