Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia.
Faculty of Arts and Sciences, Department of Mathematics, Near East University, Nicosia, Northern Cyprus, Turkey.
PLoS One. 2024 Apr 16;19(4):e0298620. doi: 10.1371/journal.pone.0298620. eCollection 2024.
In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.
在本文中，我们使用一种新颖的分段混合技术，开发了一个非线性分数阶埃博拉病毒模型，以观察具有八个腔室的动力学传播。针对具有 Arzel'a-Ascoli 和 Schauder 条件的系统，处理了分段导数的存在性和唯一性。我们研究了经典和修正分数阶微积分算子，特别是经典的 Caputo 分段算子，对模型行为的影响。模型表明，完全连续算子是一致连续的，并且根据平衡点是有界的。繁殖数 R0 是针对模型的生物可行性推导出来的，同时还进行了敏感性分析，以了解不同参数对模型的影响。敏感性分析是理解各种模型参数如何影响疾病传播的重要工具。通过对重要参数进行系统的操作，并评估它们对 Ro 的影响，我们可以更好地了解模型的弹性和敏感性。使用 Matignon 方法建立局部稳定性，使用 Lyapunov 函数建立全局稳定性，以确保所提出模型的可行解的稳定性。最后，通过使用牛顿多项式技术，针对分段 Caputo 算子，推导出数值解，并通过使用真实数据对各个分数阶的腔室进行模拟，对模型进行了仿真。我们的研究结果强调了分数阶算子在提高模型捕捉疾病复杂动态的准确性方面的重要性。这项研究有助于深入了解埃博拉病毒的动力学，并为改进疾病建模和公共卫生策略提供了有价值的见解。
