Stability Analysis of Fractional-Order SIR Model with General Incidence Rate and Treatment

Authors

  • Mohsine Aarir Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, 20650, Morocco
  • Sanaa Harroudi ENCG of Casablanca, University Hassan II, Casablanca, 20000, Morocco
  • Jaouad Danane Laboratory of Systems Modelization and Analysis for Decision Support, National School of Applied Sciences, Hassan First University, Berrechid, 26100, Morocco
  • Karam Allali Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, 20650, Morocco

Keywords:

Caputo fractional-order derivative, two-strain SIR epidemic model, general incidence function, local and global stability, treatment

Abstract

In this work, we study a fractional two-strain epidemic SI1I2R model with different incidence rates: A general incidence rate for the first strain and a bilinear incidence rate for the second strain, incorporating treatment
of each strain. The proposed model consists of four ordinary differential equations describing interactions among the susceptible, Infected and recovered individuals. Our first mathematical study focuses of proving
the existence and uniqueness of positive solutions. To show the global stability of the model equilibria, suitable Lyapunov functions are used. Numerical simulations are performed to support the analytical results
and to show the effect of the fractional derivative on convergence toward equilibria. Moreover, the role of treatment efficiency in minimizing the density of infected individuals is studied.

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Published

2026-08-01

Issue

Vol. 2026: Special Issue on Mathematical and Computational Methods in Nonlinear Systems: Theory and Applications

Section

Special Issue

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Copyright (c) 2026 Mohsine Aarir, Sanaa Harroudi, Jaouad Danane, Karam Allali

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Stability Analysis of Fractional-Order SIR Model with General Incidence Rate and Treatment. (2026). Journal of Prime Research in Mathematics, 2026, 290-308. https://jprm.sms.edu.pk/index.php/jprm/article/view/403