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Fractional-Order Model for Multi-Drug Antimicrobial Resistance

M. F. Elettreby1, 2, *, Ali S. Alqahtani1, E. Ahmed2

1 Mathematics Department, Faculty of Science, King Khalid University, Abha, 9004, Saudi Arabia.
2 Mathematics Department, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.

* Corresponding Author: M. F. Elettreby. Email: email.

(This article belongs to this Special Issue: Data Science and Modeling in Biology, Health, and Medicine)

Computer Modeling in Engineering & Sciences 2020, 124(2), 665-682.


Drug resistance is one of the most serious phenomena in financial, economic and medical terms. The present paper proposes and investigates a simple mathematical fractional-order model for the phenomenon of multi-drug antimicrobial resistance. The model describes the dynamics of the susceptible and three kinds of infected populations. The first class of the infected society responds to the first antimicrobial drug but resists to the second one. The second infected individuals react to the second antimicrobial drug but resist to the first one. The third class shows resistance to both of the two drugs. We formulate the model and associate it with some of its properties. The stability conditions of the multi-drug antimicrobial resistance equilibrium states are derived. We illustrate the analytical results by some numerical simulations.


Cite This Article

Elettreby, M. F., Alqahtani, A. S., Ahmed, E. (2020). Fractional-Order Model for Multi-Drug Antimicrobial Resistance. CMES-Computer Modeling in Engineering & Sciences, 124(2), 665–682.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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