A Fractional Two-Strain Epidemic Model with Treatment

¹ Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, 20650, Morocco
² Laboratory of Mathematics, ENCG of Casablanca, University Hassan II, Casablanca, 20000, Morocco
³ Laboratory of Systems Modelization and Analysis for Decision Support, National School of Applied Sciences, Hassan First University, Berrechid, 26100, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 13 May 2026

Abstract

In this study, we develop and examine a fractional-order epidemic model involving two strains, while taking into account treatment strategies and generalized incidence rates. The transmission dynamics of the two strains are described by two nonlinear incidence functions f (S, I₁)I₁ h (S, I₂)I₂ allowing the model to capture more realistic infection mechanisms beyond the classical bilinear form. The proposed model is formulated as a system of four Caputo fractional differential equations describing the interactions among susceptible, infected, and recovered individuals. Initially, it is established that solutions exist, are unique, positive and bounded. Next, the basic reproduction numbers corresponding to each strain are computed using the next-generation matrix approach. The existence of both the disease-free and endemic equilibrium states is analyzed, and sufficient conditions for their global stability are established through appropriate Lyapunov functionals. Finally, numerical simulations are performed to support the analytical results and to demonstrate the impact of the fractional-order derivative on the system’s convergence behavior. The role of treatment strategies in limiting the spread of the infection is also examined.