Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption

Mouhcine Naim; Yassine Sabbar; Anwar Zeb

doi:10.53391/mmnsa.2022.013

Authors

Mouhcine Naim Laboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morocco https://orcid.org/0000-0002-6130-3633
Yassine Sabbar LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco https://orcid.org/0000-0002-1127-4395
Anwar Zeb Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Khyber Pakhtunkhwa, Pakistan https://orcid.org/0000-0002-5460-3718

DOI:

https://doi.org/10.53391/mmnsa.2022.013

Keywords:

Viral model, non-cytolytic, immunity, fractional-order formulation, stability

Abstract

This article deals with a Caputo fractional-order viral model that incorporates the non-cytolytic immune hypothesis and the mechanism of viral replication inhibition. Firstly, we establish the existence, uniqueness, non-negativity, and boundedness of the solutions of the proposed viral model. Then, we point out that our model has the following three equilibrium points: equilibrium point without virus, equilibrium state without immune system, and equilibrium point activated by immunity with humoral feedback. By presenting two critical quantities, the asymptotic stability of all said steady points is examined. Finally, we examine the finesse of our results by highlighting the impact of fractional derivatives on the stability of the corresponding steady points.

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