Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity

Year 2024, Volume: 4 Issue: 5-Special Issue: ICAME'24, 94 - 115, 31.12.2024

Mouhcine Naim , Anwar Zeb , Ahmed Ali Mohsen , Yassine Sabbar , Mustafa Yıldız

https://doi.org/10.53391/mmnsa.1517325

Abstract

A fractional viral model is proposed in this work, as fractional-order calculus is considered more suitable than integer-order calculus for modeling virological systems with inherent memory and long-range interactions. The model incorporates virus-to-cell infection, cell-to-cell transmission, cure rate, and humoral immunity. Additionally, the non-lytic immunological mechanism, which prevents viral reproduction and reduces cell infection, is included. Caputo fractional derivatives are utilized in each compartment to capture long-term memory effects and non-local behavior. It is demonstrated that the model has nonnegative and bounded solutions. Three equilibrium states are identified in the improved viral model: the virus-clear steady state $\mathcal{G}^{\circ }$, the immunity-free steady state $\mathcal{G}_{1}^{\star}$ and the infection steady state with humoral immunity $\mathcal{G}_{2}^{\star }$. The local stability of the equilibria is investigated using the Routh-Hurwitz criteria and the Matignon condition, while the global stability is shown through the Lyapunov approach and the fractional LaSalle invariance principle. Finally, the theoretical conclusions are validated by numerous numerical simulations.

Keywords

Infection model, fractional-order model, non-lytic humoral immunity, stability

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