Fractional dynamics and cost-effective control strategies for measles transmission

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.

Keywords

Fractional epidemic model / Measles transmission / Vaccination behavior / Optimal control / Memory effects / Cost-effectiveness analysis

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