Yu Fang, Younas Khan Muhammad, Bilal Riaz Muhammad, Ullah Saif, Farooq Muhammad
School of Mathematics and Data Sciences, Changji University, Changji, Xinjiang, China.
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan.
PLoS One. 2025 Jan 14;20(1):e0309360. doi: 10.1371/journal.pone.0309360. eCollection 2025.
In biology and life sciences, fractal theory and fractional calculus have significant applications in simulating and understanding complex problems. In this paper, a compartmental model employing Caputo-type fractional and fractal-fractional operators is presented to analyze Nipah virus (NiV) dynamics and transmission. Initially, the model includes nine nonlinear ordinary differential equations that consider viral concentration, flying fox, and human populations simultaneously. The model is reconstructed using fractional calculus and fractal theory to better understand NiV transmission dynamics. We analyze the model's existence and uniqueness in both contexts and instigate the equilibrium points. The clinical epidemiology of Bangladesh is used to estimate model parameters. The fractional model's stability is examined using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. Moreover, interpolation methods are used to construct computational techniques to simulate the NiV model in fractional and fractal-fractional cases. Simulations are performed to validate the stable behavior of the model for different fractal and fractional orders. The present findings will be beneficial in employing advanced computational approaches in modeling and control of NiV outbreaks.
在生物学和生命科学领域，分形理论和分数阶微积分在模拟和理解复杂问题方面具有重要应用。本文提出了一个采用卡普托型分数阶和分形 - 分数阶算子的房室模型，用于分析尼帕病毒（NiV）的动力学和传播。最初，该模型包含九个非线性常微分方程，同时考虑了病毒浓度、狐蝠和人类种群。利用分数阶微积分和分形理论对该模型进行重构，以更好地理解NiV传播动力学。我们分析了该模型在两种情况下的存在性和唯一性，并研究了平衡点。利用孟加拉国的临床流行病学数据来估计模型参数。使用乌拉姆 - 海尔斯稳定性和乌拉姆 - 海尔斯 - 拉西亚斯稳定性来检验分数阶模型的稳定性。此外，采用插值方法构建计算技术，以模拟分数阶和分形 - 分数阶情况下的NiV模型。进行模拟以验证该模型在不同分形阶和分数阶下的稳定行为。目前的研究结果将有助于在NiV疫情的建模和控制中采用先进的计算方法。
