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Article

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

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School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
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Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada
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Department of Mathematics, Huzhou University, Huzhou 313000, China
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Department of Banking and Finance, FEMA, University of Malta, MSD 2080 Msida, Malta
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European University Institute, Department of Economics, Via delle Fontanelle, 18, I-50014 Florence, Italy
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Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha 410081, China
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Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 26 March 2021 / Revised: 30 April 2021 / Accepted: 12 May 2021 / Published: 14 May 2021
Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated. View Full-Text
Keywords: HIV model; treatment compartment; Caputo–Fabrizio fractional; optimal control; sensitivity analysis HIV model; treatment compartment; Caputo–Fabrizio fractional; optimal control; sensitivity analysis
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MDPI and ACS Style

Wang, H.; Jahanshahi, H.; Wang, M.-K.; Bekiros, S.; Liu, J.; Aly, A.A. A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies. Entropy 2021, 23, 610. https://0-doi-org.brum.beds.ac.uk/10.3390/e23050610

AMA Style

Wang H, Jahanshahi H, Wang M-K, Bekiros S, Liu J, Aly AA. A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies. Entropy. 2021; 23(5):610. https://0-doi-org.brum.beds.ac.uk/10.3390/e23050610

Chicago/Turabian Style

Wang, Hua, Hadi Jahanshahi, Miao-Kun Wang, Stelios Bekiros, Jinping Liu, and Ayman A. Aly. 2021. "A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies" Entropy 23, no. 5: 610. https://0-doi-org.brum.beds.ac.uk/10.3390/e23050610

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