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ARTICLE

Fractional-Order Model for Multi-Drug Antimicrobial Resistance

M. F. Elettreby^{1, 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: .

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

Computer Modeling in Engineering & Sciences 2020, 124(2), 665-682. https://doi.org/10.32604/cmes.2020.09194

Received 20 November 2019; Accepted 06 March 2020; Issue published 20 July 2020

Abstract

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.

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Citations