Lamwong Jiraporn, Pongsumpun Puntani
Department of Applied Basic Subjects, Thatphanom College, Nakhon Phanom University, Nakhon Phanom, 48000, Thailand.
Department of Mathematics, School of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, 10520, Thailand.
Comput Biol Med. 2025 Aug;194:110476. doi: 10.1016/j.compbiomed.2025.110476. Epub 2025 Jun 10.
Dengue fever remains a critical public health concern, particularly in regions like Thailand, where the disease exhibits complex transmission dynamics involving human and mosquito populations. Traditional models often fail to address the intricacies of non-local interactions, memory effects, and control dynamics. This research introduces an innovative approach using fractional optimal control problems (FOCPs) integrated with the Atangana-Baleanu fractional derivative in the Caputo sense. The model stratifies human and mosquito populations into detailed compartments, enabling a granular representation of transmission dynamics. The FOCP framework leverages fractional-order equations to incorporate memory-dependent and non-local interactions, ensuring biological feasibility and predictive accuracy. Computational results reveal that the model aligns closely with observed data for dengue fever, dengue hemorrhagic fever, and dengue shock syndrome across fractional orders ranging from 0.83 to 1.00. Sensitivity analyses identify critical parameters, such as biting rates and initial population sizes, as pivotal to disease control. The findings underscore the effectiveness of FOCPs in optimizing public health interventions, offer a robust tool for minimizing infection rates and associated costs. The theoretical global stability analysis confirms the model's reliability in predicting long-term outcomes under varying epidemiological scenarios. Future research could extend this framework to incorporate environmental variables, co-infections, and vaccination strategies, enhancing its applicability across diverse public health challenges. This study represents a significant step forward in the mathematical modeling of epidemic diseases, particularly in optimizing control measures for dengue fever.
登革热仍然是一个严重的公共卫生问题，特别是在泰国等地区，该疾病呈现出涉及人类和蚊子种群的复杂传播动态。传统模型往往无法解决非局部相互作用、记忆效应和控制动态的复杂性。本研究引入了一种创新方法，即使用与Caputo意义下的阿坦加纳-巴莱亚努分数阶导数相结合的分数阶最优控制问题（FOCPs）。该模型将人类和蚊子种群细分为详细的 compartments，从而能够对传播动态进行细致的描述。FOCP框架利用分数阶方程纳入依赖记忆和非局部相互作用，确保生物学可行性和预测准确性。计算结果表明，该模型在0.83至1.00的分数阶范围内与登革热、登革出血热和登革休克综合征的观测数据密切吻合。敏感性分析确定了关键参数，如叮咬率和初始种群规模，对疾病控制至关重要。研究结果强调了FOCPs在优化公共卫生干预措施方面的有效性，为降低感染率和相关成本提供了一个强大的工具。理论上的全局稳定性分析证实了该模型在预测不同流行病学情景下的长期结果方面的可靠性。未来的研究可以扩展这个框架，纳入环境变量、共感染和疫苗接种策略，提高其在应对各种公共卫生挑战方面的适用性。这项研究在传染病数学建模方面迈出了重要一步，特别是在优化登革热控制措施方面。
