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.

中文翻译：

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通过包含分数阶导数的系统镜头观察媒介传播疾病的动力学

本文通过包含分数阶导数的系统的镜头，探讨了蚊子传播的媒介传播疾病的动态。具体来说，我们通过引入具有 Caputo 感知导数的分数阶系统来扩展经典的 SISUV 和 SIRUV 模型。这种增强将记忆效应引入建模过程。我们的研究深入研究了两种模型的局部和全局稳定性分析，为这些疾病的动态提供了宝贵的见解。为了验证我们的理论结果，我们进行了数值模拟，确认了所提出模型的稳健性和适用性。