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<p>Measles, a highly contagious and potentially fatal viral disease, has been recognized for decades, and several modeling techniques for measles are available. In recent years, fractional calculus has become increasingly popular in a variety of medical areas. This paper provides a comprehensive analysis of a fractional-order mathematical model for the measles epidemic, employing the constant proportional Caputo–Fabrizio operator to demonstrate the complex impacts of the infection on society and how people respond to vaccination. The feasibility region and equilibrium points of the system are determined, followed by an examination of the global stability of the equilibrium points. The study examines both the basic reproductive number and its extension, the strength number. We also perform a sensitivity analysis on each parameter to highlight its potential impact on the reproductive number. The fractional-order Laplace Adomian Decomposition Method is used to generate iterative solutions. Picard’s stable condition from the fixed point theorem is used to ensure that the precise solution is unique. We also present an additional detailed investigation of the hybrid operator. To evaluate the computational efficiency and accuracy of the fractional-order model, we compare numerical solutions with the classical integer-order model. The results show that the hybrid fractional derivative technique works better in terms of classification accuracy in measles propagation than standard derivative models.</p>

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Assessment and comparison of nonsingular kernels in various contexts for the measles epidemic model

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Kottakkaran Sooppy Nisar,
  • Muhammad Farman

摘要

Measles, a highly contagious and potentially fatal viral disease, has been recognized for decades, and several modeling techniques for measles are available. In recent years, fractional calculus has become increasingly popular in a variety of medical areas. This paper provides a comprehensive analysis of a fractional-order mathematical model for the measles epidemic, employing the constant proportional Caputo–Fabrizio operator to demonstrate the complex impacts of the infection on society and how people respond to vaccination. The feasibility region and equilibrium points of the system are determined, followed by an examination of the global stability of the equilibrium points. The study examines both the basic reproductive number and its extension, the strength number. We also perform a sensitivity analysis on each parameter to highlight its potential impact on the reproductive number. The fractional-order Laplace Adomian Decomposition Method is used to generate iterative solutions. Picard’s stable condition from the fixed point theorem is used to ensure that the precise solution is unique. We also present an additional detailed investigation of the hybrid operator. To evaluate the computational efficiency and accuracy of the fractional-order model, we compare numerical solutions with the classical integer-order model. The results show that the hybrid fractional derivative technique works better in terms of classification accuracy in measles propagation than standard derivative models.