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Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives

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  • Skwara, Urszula
  • Mozyrska, Dorota
  • Aguiar, Maira
  • Stollenwerk, Nico

Abstract

This paper explores the dynamics of vector-borne diseases transmitted by mosquitoes through the lens of systems incorporating fractional-order derivatives. Specifically, we extend the classical SISUV and SIRUV models by introducing fractional-order systems with the Caputo sense derivative. This augmentation introduces memory effects into the modelling process. Our study delves into the local and global stability analyses of both models, providing valuable insights into the dynamics of these diseases. To validate our theoretical results, we conduct numerical simulations confirming the robustness and applicability of the proposed models.

Suggested Citation

  • Skwara, Urszula & Mozyrska, Dorota & Aguiar, Maira & Stollenwerk, Nico, 2024. "Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001942
    DOI: 10.1016/j.chaos.2024.114643
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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Al-khedhairi, A. & Elsadany, A.A. & Elsonbaty, A., 2019. "Modelling immune systems based on Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 25-39.
    4. Ilhan, Esin & Veeresha, P. & Baskonus, Haci Mehmet, 2021. "Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
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