Mathematical analysis of a fractional-order influenza model with resistant and non-resistant strains

Document Type : Research Article

Authors

Ismail Aamoum ¹

Adil Meskaf ^{1, 2}

Zakaria Yaagoub ^{3, 4}

El Mehdi Farah ⁵

¹ Experimental Laboratory of Innovation in Technology and Simulations, Chouaib Doukkali University, El Jadida, Morocco.

² Department of Economics and Management (SEG), Faculty of Legal, Economic and Social Sciences, Chouaib Doukkali University, El Jadida, Morocco.

³ National School of Public Health, Ministry of Health and Social Protection, Rabat, Morocco.

⁴ Department of Computer Science, Faculty of Sciences, Mohammed V University in Rabat, Morocco.

⁵ Applied Mathematics Team EMA, Laboratory of Advanced Research in Industrial and Logistics Engineering (LARILE), National Higher School of Electricity and Mechanics (ENSEM), Hassan II University of Casablanca, Morocco.

10.22067/ijnao.2026.96816.1791

Abstract

There are numerous acute viral infections in the world. The influenza virus is the cause of influenza, a respiratory illness. In the twenty-first century, fractional-order derivative modeling of infectious diseases has gained popularity. In the research publications, a number of fractional-order derivative models have been built. We provide a fractional two-strain influenza epidemic model in this research, which incorporates both resistant and non-resistant strains. We prove the existence and uniqueness of the global positive solution. The equilibrium points and the basic reproduction number are obtained. We study the global stability of our equilibrium points using some Lyapunov functions and LaSalle invariant principal. Finally, a series of numerical simulations is presented to demonstrate the behavior of the model and to verify our theoretical results. They show that although the order of the fractional derivatives does not affect the stability of the equilibrium states, it plays an important role in the speed at which the system converges to these equilibria.

Keywords

Fractional order

Influenza

Basic reproduction number

Global stability

Two-strain

Subjects

• Modeling and Simulation

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