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<p>This work develops a fractional-order epidemic model to explore the dynamics of measles transmission, with particular emphasis on the roles of immune failure and waning immunity. We rigorously establish the existence, uniqueness, boundedness, and nonnegativity of the solutions. Additionally, we analyze the equilibrium points and provide criteria for their local stability, using the basic reproduction number as a key metric. A comprehensive sensitivity analysis systematically evaluates the impact of each parameter, ranking the principal epidemiological determinants. To validate the model, we simulated the measles outbreak in Australia from 1994 to 2023. The results show that the fractional-order model, optimized to an order of 0.94, significantly improves the fit to real-world data. Furthermore, our findings reveal that increasing the strength of memory effects may exert opposite influences on the sizes of the immune-failure population and the infected population.</p>

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Modeling and analysis of measles epidemic model with memory effect

  • 期刊论文

  • 发表日期：

    2025年8月29日

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  • Denghao Pang,
  • Xiuyang Wu,
  • Chong Li,
  • Zhenkun Wang

摘要

This work develops a fractional-order epidemic model to explore the dynamics of measles transmission, with particular emphasis on the roles of immune failure and waning immunity. We rigorously establish the existence, uniqueness, boundedness, and nonnegativity of the solutions. Additionally, we analyze the equilibrium points and provide criteria for their local stability, using the basic reproduction number as a key metric. A comprehensive sensitivity analysis systematically evaluates the impact of each parameter, ranking the principal epidemiological determinants. To validate the model, we simulated the measles outbreak in Australia from 1994 to 2023. The results show that the fractional-order model, optimized to an order of 0.94, significantly improves the fit to real-world data. Furthermore, our findings reveal that increasing the strength of memory effects may exert opposite influences on the sizes of the immune-failure population and the infected population.