Non-optimal and optimal fractional control analysis of measles using real data

Abstract

This study employs fractional, non-optimal, and optimal control techniques to analyze measles transmission dynamics using real-world data. Thus, we develop a fractional-order compartmental model capturing measles transmission dynamics. We then formulate an optimal control problem to minimize the disease burden while considering constraints such as vaccination resources and intervention costs. The proposed model’s positivity, boundedness, measles reproduction number, and stability are obtained. The sensitivity analysis using the partial rank correlation coefficient is shown for the fractional orders of 0.99 and 0.90. It is noticed that the rate of recruitment into the susceptible population ($\pi$), the rate at which individuals in the latent class become asymptomatic (${\alpha }_1$), and the transmission rate ($\beta$) contribute positively to the spread of the disease, while the rate at which individuals in the asymptomatic class become symptomatic (${\alpha }_2$), the vaccination rate for the first measles dose (${\gamma }_1$), and the rate at which individuals in the latent class recover from measles (${\delta }_1$) contribute significantly to the reduction of measles in the community. Utilizing numerical simulations and sensitivity analyses, we identify optimal control strategies that balance the trade-offs between intervention efficacy, resource allocation, and societal costs. Our findings provide insights into the effectiveness of fractional optimal control strategies in mitigating measles outbreaks and contribute to developing more robust and adaptive disease control policies in real-world scenarios.