Optimal Control Applied to Piecewise-Fractional Ebola Model

Silvério Rosa () and Faïçal Ndaïrou
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Silvério Rosa: Instituto de Telecomunicações and Department of Mathematics, University of Beira Interior, 6201-001 Covilhã, Portugal
Faïçal Ndaïrou: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2024, vol. 12, issue 7, 1-14

Abstract: A recently proposed fractional-order mathematical model with Caputo derivatives was developed for Ebola disease. Here, we extend and generalize this model, beginning with its correction. A fractional optimal control (FOC) problem is then formulated and numerically solved with the rate of vaccination as the control measure. The research presented in this work addresses the problem of fitting real data from Guinea, Liberia, and Sierra Leone, available at the World Health Organization (WHO). A cost-effectiveness analysis is performed to assess the cost and effectiveness of the control measure during the intervention. We come to the conclusion that the fractional control is more efficient than the classical one only for a part of the time interval. Hence, we suggest a system where the derivative order changes over time, becoming fractional or classical when it makes more sense. This type of variable-order fractional model, known as piecewise derivative with fractional Caputo derivatives, is the most successful in managing the illness.

Keywords: Ebola; compartmental mathematical models; fractional-order optimal control; piecewise derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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