An Effective Application of Fractional Optimal Control in the Treatment of Infectious Diseases
Subject Areas : electrical and computer engineering
Amin Jajarmi
1
(Department of Electrical Engineering, Faculty of Engineering, University of Bojnord, Bojnord, Iran)
Manijeh Hasanabadi
2
(Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran)
Keywords: Infection transmission dynamics of HIV, optimal control, fractional derivatives, numerical results,
Abstract :
In this paper, a novel optimal control model is proposed using the generalized fractional derivative with an arbitrary kernel function to investigate and control HIV infection. Accordingly, an effective therapeutic strategy based on the fractional optimal control theory is formulated and examined for the mentioned disease. The optimality conditions, based on the principle of Pontryagin’s maximization, are formulated as a fractional boundary value problem. Furthermore, an efficient numerical method is presented for finding the solution to the generalized fractional dynamic system and solving the corresponding optimal control problem. Convergence and analysis of the proposed technique’s error are also studied and evaluated. Numerical simulations demonstrate that the fractional derivative model for a fractional order of 0.99 exhibits lower error and, consequently, better accuracy compared to the integer order model and other fractional orders tested (based on real data validated by the World Health Organization). Moreover, the implementation of the proposed optimal control leads to a significant reduction in the spread of the disease. Consequently, the introduced fractional model serves as an efficient tool for highlighting the fundamental characteristics of the transmission of the aforementioned disease and can enhance the effectiveness of therapeutic strategies.
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