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The Role of Partial Immunity in Dengue Transmission: A Fractional Derivative Perspective

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  • Takasar Hussain
  • Sohail Ahmad
  • Ahmed M. Zidan
  • Asfandyar Khan
  • Gul Rahmat
  • Rasool Shah

Abstract

In this study, we discuss a comprehensive dynamical model incorporating fractional calculus to analyze spread of dengue disease, accounting for partial immunity, transmission probabilities, and various control measures. The model extends traditional integer‐order approaches by introducing a fractional order system, which captures memory effects and more accurately represents real‐world transmission dynamics. We explore the impact of losing immunity and mosquito biting rates, alongside vaccination and treatment rates, on the disease dynamics. The basic reproduction number (R0) is derived and used to examine constant solutions and their stability, providing insights into the threshold conditions for disease eradication or persistence. Utilizing the Volterra‐type representation, we further investigate the temporal evolution of the disease, highlighting the significance of the memory index and its influence on long‐term behavior. A novel numerical scheme is employed for outcomes of a fractional model, ensuring accuracy and efficiency in capturing the complex interplay between different factors. The results indicate that partial immunity and the memory index significantly affect the stability of equilibria and the effectiveness of vaccination strategies.

Suggested Citation

  • Takasar Hussain & Sohail Ahmad & Ahmed M. Zidan & Asfandyar Khan & Gul Rahmat & Rasool Shah, 2025. "The Role of Partial Immunity in Dengue Transmission: A Fractional Derivative Perspective," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:3196877
    DOI: 10.1155/jom/3196877
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    References listed on IDEAS

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    1. Dennis L Chao & Ira M Longini Jr & M Elizabeth Halloran, 2013. "The Effects of Vector Movement and Distribution in a Mathematical Model of Dengue Transmission," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-6, October.
    2. Jan, Rashid & Khan, Muhammad Altaf & Kumam, Poom & Thounthong, Phatiphat, 2019. "Modeling the transmission of dengue infection through fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 189-216.
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