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

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

doi:10.53391/mmnsa.1517325

EN

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

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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Details

Primary Language

English

Subjects

Biological Mathematics

Journal Section

Research Article

Authors

Mouhcine Naim ^*
0000-0002-6130-3633
Morocco

Anwar Zeb
0000-0002-5460-3718
Pakistan

Ahmed Ali Mohsen
0000-0003-3812-8918
Iraq

Yassine Sabbar
0000-0002-1127-4395
Morocco

Mustafa Yıldız
0000-0003-3367-7176
Türkiye

Publication Date

December 31, 2024

Submission Date

July 16, 2024

Acceptance Date

December 27, 2024

Published in Issue

Year 2024 Volume: 4 Number: 5-Special Issue: ICAME'24

DOI

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

IZ

https://izlik.org/JA93NH89CA

APA

Naim, M., Zeb, A., Mohsen, A. A., Sabbar, Y., & Yıldız, M. (2024). Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity. Mathematical Modelling and Numerical Simulation With Applications, 4(5-Special Issue: ICAME’24), 94-115. https://doi.org/10.53391/mmnsa.1517325

AMA

1.Naim M, Zeb A, Mohsen AA, Sabbar Y, Yıldız M. Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity. MMNSA. 2024;4(5-Special Issue: ICAME’24):94-115. doi:10.53391/mmnsa.1517325

Chicago

Naim, Mouhcine, Anwar Zeb, Ahmed Ali Mohsen, Yassine Sabbar, and Mustafa Yıldız. 2024. “Local and Global Stability of a Fractional Viral Infection Model With Two Routes of Propagation, Cure Rate and Non-Lytic Humoral Immunity”. Mathematical Modelling and Numerical Simulation With Applications 4 (5-Special Issue: ICAME’24): 94-115. https://doi.org/10.53391/mmnsa.1517325.

EndNote

Naim M, Zeb A, Mohsen AA, Sabbar Y, Yıldız M (December 1, 2024) Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity. Mathematical Modelling and Numerical Simulation with Applications 4 5-Special Issue: ICAME’24 94–115.

IEEE

[1]M. Naim, A. Zeb, A. A. Mohsen, Y. Sabbar, and M. Yıldız, “Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity”, MMNSA, vol. 4, no. 5-Special Issue: ICAME’24, pp. 94–115, Dec. 2024, doi: 10.53391/mmnsa.1517325.

ISNAD

Naim, Mouhcine - Zeb, Anwar - Mohsen, Ahmed Ali - Sabbar, Yassine - Yıldız, Mustafa. “Local and Global Stability of a Fractional Viral Infection Model With Two Routes of Propagation, Cure Rate and Non-Lytic Humoral Immunity”. Mathematical Modelling and Numerical Simulation with Applications 4/5-Special Issue: ICAME’24 (December 1, 2024): 94-115. https://doi.org/10.53391/mmnsa.1517325.

JAMA

1.Naim M, Zeb A, Mohsen AA, Sabbar Y, Yıldız M. Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity. MMNSA. 2024;4:94–115.

MLA

Naim, Mouhcine, et al. “Local and Global Stability of a Fractional Viral Infection Model With Two Routes of Propagation, Cure Rate and Non-Lytic Humoral Immunity”. Mathematical Modelling and Numerical Simulation With Applications, vol. 4, no. 5-Special Issue: ICAME’24, Dec. 2024, pp. 94-115, doi:10.53391/mmnsa.1517325.

Vancouver

1.Mouhcine Naim, Anwar Zeb, Ahmed Ali Mohsen, Yassine Sabbar, Mustafa Yıldız. Local and global stability of a fractional viral infection model with two routes of propagation, cure rate and non-lytic humoral immunity. MMNSA. 2024 Dec. 1;4(5-Special Issue: ICAME’24):94-115. doi:10.53391/mmnsa.1517325

Math Model Numer Simul Appl - 2025

The published articles in MMNSA are licensed under a Creative Commons Attribution 4.0 International License

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

Abstract

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

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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