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RESEARCH ARTICLE

Fractional dynamics and cost-effective control strategies for measles transmission

Asiyeh Ebrahimzadeh1 ,  Amin Jajarmi2,3*
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1 Department of Mathematics, Faculty of Education and Graduate Studies, Farhangian University, Tehran, Iran
2 Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran
3 Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India
IJOCTA, 025390160 https://doi.org/10.36922/IJOCTA025390160
Received: 23 September 2025 | Revised: 3 November 2025 | Accepted: 10 November 2025 | Published online: 16 December 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Despite the proven effectiveness of measles vaccines, suboptimal coverage and changing public behavior continue to pose challenges for eradication efforts worldwide. This study develops a fractional-order compartmental model to capture measles transmission dynamics while accounting for memory effects and adaptive behavioral responses to vaccination campaigns. Using Caputo fractional derivatives, the model reflects the non-local and history-dependent nature of disease spread more realistically than classical integer-order models. Four time-dependent control strategies—early newborn vaccination, adult catch-up immunization, administration of a second vaccine dose, and early treatment of exposed individuals—are incorporated and optimized through Pontryagin’s Maximum Principle adapted for fractional systems. A sensitivity analysis of the basic reproduction number shows which parameters have the biggest effect on the potential for an outbreak. Numerical simulations demonstrate that fractional dynamics significantly modify infection peaks, outbreak duration, and total intervention costs compared to classical models. The results emphasize that integrating memory effects and behavioral feedback can enhance the design of vaccination programs and inform more cost-effective public health policies for measles mitigation.

Graphical abstract
Keywords
Fractional epidemic model
Measles transmission
Vaccination behavior
Optimal control
Memory effects
Cost-effectiveness analysis
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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