Dhar Biplab, Sajid Mohammad
Applied Science Cluster - Mathematics, UPES, Dehradun, UK, India.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah, Saudi Arabia.
Sci Rep. 2025 Mar 28;15(1):10785. doi: 10.1038/s41598-025-95548-z.
Healthcare reporting methods have seen a common problem with actual incidence of scrub typhus cases in Northeast India that were reported during post rainy season. We propose a Host-Vector model, a first of its kind, with a significant modification in the disease infection transmission rate. Our work aims to investigate a mathematical model by Atangana-Baleanu fractal-fractional operator that has seasonal pattern incorporating 2010-2022 data. The existence-uniqueness property is investigated using the fixed point theory, and also Ulam-Hyers stability is performed. Based on Lagrange's interpolation polynomial in the numerical scheme, a numerical investigation for various values of the fractional parameters is presented. The numerical simulation and phase plane trajectories demonstrates excellent performance of the suggested model as the number of individuals who recover rises gradually after herd immunity threshold points and turning points. Furthermore, the information gathered here may be useful for enhancing spatiotemporally dynamic scrub typhus disease models.
医疗保健报告方法在印度东北部雨季过后报告的恙虫病实际发病率方面存在一个常见问题。我们提出了一种宿主-媒介模型，这是同类模型中的首个，对疾病感染传播率进行了重大修改。我们的工作旨在研究一个由阿坦加纳-巴莱努分数阶算子构建的数学模型，该模型具有纳入2010 - 2022年数据的季节性模式。使用不动点理论研究存在唯一性性质，并进行了乌拉姆-海尔斯稳定性分析。基于数值方案中的拉格朗日插值多项式，给出了分数参数不同值的数值研究。数值模拟和相平面轨迹表明，随着群体免疫阈值点和转折点后康复个体数量逐渐增加，所提出的模型具有出色的性能。此外，这里收集的信息可能有助于增强时空动态恙虫病模型。
