The impact of Caputo-Fabrizio operator on the complex dynamics of a multidrug resistance model

Ahmed Ezzat Matouk; Ahmed Ezzat Matouk

doi:10.3934/math.2026356

AIMS Mathematics

2026, Volume 11, Issue 3: 8655-8676. doi: 10.3934/math.2026356

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Research article

The impact of Caputo-Fabrizio operator on the complex dynamics of a multidrug resistance model

Ahmed Ezzat Matouk ^{1,2
,
,}

1.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia
2.
College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Received: 29 January 2026 Revised: 11 March 2026 Accepted: 19 March 2026 Published: 31 March 2026
MSC : 34H10, 34C28, 37M05

This work studied the impact of Caputo–Fabrizio derivatives on the chaotic dynamics in a multidrug resistance dynamical system. The local stability conditions of the drug-free, healthy, and multidrug resistance equilibrium states are proven. The numerical simulations demonstrate the presence of chaos in the considered fractional model and its integer-order counterpart, which means that the coexistence of both susceptible and infected populations is highly unpredictable because of the multidrug resistance. Furthermore, the consistency between the fractional system and its integer-order counterpart is evident for a wide time scale, despite the use of two different numerical algorithms. The new numerical algorithm for integrating the fractional model is presented, along with proofs of its conditional stability and convergence. In addition, the study used advanced software tools, such as bifurcation diagrams based on the local maxima algorithm and Lyapunov spectrum, that confirm the regions of chaos and their distribution in these systems when the growth rate of the susceptible population changes within a certain range.
- antimicrobial resistance,
- Caputo-Fabrizio,
- stability,
- chaos
Citation: Ahmed Ezzat Matouk. The impact of Caputo-Fabrizio operator on the complex dynamics of a multidrug resistance model[J]. AIMS Mathematics, 2026, 11(3): 8655-8676. doi: 10.3934/math.2026356

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Abstract

This work studied the impact of Caputo–Fabrizio derivatives on the chaotic dynamics in a multidrug resistance dynamical system. The local stability conditions of the drug-free, healthy, and multidrug resistance equilibrium states are proven. The numerical simulations demonstrate the presence of chaos in the considered fractional model and its integer-order counterpart, which means that the coexistence of both susceptible and infected populations is highly unpredictable because of the multidrug resistance. Furthermore, the consistency between the fractional system and its integer-order counterpart is evident for a wide time scale, despite the use of two different numerical algorithms. The new numerical algorithm for integrating the fractional model is presented, along with proofs of its conditional stability and convergence. In addition, the study used advanced software tools, such as bifurcation diagrams based on the local maxima algorithm and Lyapunov spectrum, that confirm the regions of chaos and their distribution in these systems when the growth rate of the susceptible population changes within a certain range.

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