Verma Lalchand, Meher Ramakanta, Nikan Omid, Al-Saedi Akeel A
Department of Applied Sciences and Humanities, Panipat Institute of Engineering and Technology, Samalkha, Panipat, Haryana, 132102, India.
Department of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat, Surat, Gujarat, 395 007, India.
Sci Rep. 2025 Aug 21;15(1):30677. doi: 10.1038/s41598-025-16599-w.
This paper focuses on a combined SIR-SI epidemic model to evaluate the transmission dynamics of dengue fever, integrating the susceptible-infected-recovered (SIR) framework for the human population with the susceptible-infected (SI) framework for mosquitoes. The model is formulated as a system of nonlinear differential equations and is further extended by incorporating fractional-order derivatives in the Caputo sense to capture memory effects in disease transmission. A thorough investigation of the disease-free and endemic equilibrium points is conducted, encompassing both local and global stability at the disease-free state. The basic reproduction number, [Formula: see text], is derived, and a sensitivity analysis is performed to identify the key parameters influencing the transmission dynamics. To ensure mathematical rigor, the existence and uniqueness of the model's solutions are also examined. For numerical approximation, the two-step Lagrange polynomial method is applied, enabling simulation of the model under various fractional orders and parameter settings. The results demonstrate that the fractional-order approach offers deeper insights into the dynamics of dengue transmission, highlighting the importance of memory effects. These findings provide valuable guidance for medical professionals, policymakers, and public health authorities in designing more effective control strategies.
本文聚焦于一个用于评估登革热传播动力学的SIR-SI组合流行病模型，该模型将人类群体的易感-感染-康复（SIR）框架与蚊子的易感-感染（SI）框架相结合。该模型被表述为一个非线性微分方程组，并通过纳入Caputo意义下的分数阶导数进行进一步扩展，以捕捉疾病传播中的记忆效应。对无病平衡点和地方病平衡点进行了全面研究，包括无病状态下的局部稳定性和全局稳定性。推导了基本再生数[公式：见原文]，并进行了敏感性分析以确定影响传播动力学的关键参数。为确保数学严谨性，还研究了模型解的存在性和唯一性。对于数值近似，应用了两步拉格朗日多项式方法，能够在各种分数阶和参数设置下对模型进行模拟。结果表明，分数阶方法为登革热传播动力学提供了更深入的见解，突出了记忆效应的重要性。这些发现为医学专业人员、政策制定者和公共卫生当局设计更有效的控制策略提供了有价值的指导。
