Raza Muhammad Aon, Agama Fekadu Tesgera, Sultana Sobia, Rashid Saima, Alharthi Mohammed Shaaf
Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan.
Department of Mathematics, Wollega University, 395, Nekemte, Ethiopia.
Sci Rep. 2025 Apr 28;15(1):14872. doi: 10.1038/s41598-025-89286-5.
Cholera is a life-threatening form of diarrhoea resulting from a bacterial infection of the gastrointestinal system caused by Vibrio cholerae. The aim of this article is to explore the dynamic characteristics of cholera disease transmission and the equilibrium level of recovery in a stochastic cholera framework by adopting piecewise fractional differential operator approaches. Firstly, we provide a detailed fractional-order form of the cholera model, showing the system's positivity and boundedness. Meanwhile, equilibrium analysis is performed to comprehend the model's behaviour and stability for disease-free as well as endemic-free equilibrium. Bacterial development rates have been reported to correlate with the Allee phenomenon. The resulting system exhibits multi-stability for forward and saddle-node bifurcations based on various settings. Global sensitivity is calculated employing the partial rank correlation coefficient approach. Furthermore, the model analyzes a stochastic fractional cholera system. Through a rigorous analysis, we demonstrate that the stochastic model offers a unique global positive solution. Lyapunov function theory is used to create criteria that ensure the model's unique erogodic stationary distribution at [Formula: see text]. Afterwards, the phenomenon that excessive noises can result in the elimination of cholera is discovered. Moreover, this model enables us to study a range of behaviors, from bridging to unpredictability, helping us to understand and predict the process from the beginning to the end of the virus. Moreover, the piecewise differential operators have chosen to extend novel pathways for researchers across several fields, enabling them to convey unique features in various time periods. These operators can be gathered with classical, Caputo, Atangana-Baleanu-Caputo fractional derivative, and random perturbation. As a result, the analytical insights are validated using computational modeling, providing a novel viewpoint on spreading diseases in a societal environment.
霍乱是一种由霍乱弧菌引起的胃肠道系统细菌感染导致的危及生命的腹泻形式。本文的目的是通过采用分段分数阶微分算子方法，在随机霍乱框架中探索霍乱疾病传播的动态特征和恢复的平衡水平。首先，我们给出了霍乱模型的详细分数阶形式，展示了系统的正性和有界性。同时，进行平衡分析以理解模型对于无病平衡和地方病平衡的行为及稳定性。据报道细菌生长速率与阿利效应相关。基于各种设定，所得系统表现出前向和鞍结分岔的多重稳定性。采用偏秩相关系数方法计算全局敏感性。此外，该模型分析了一个随机分数阶霍乱系统。通过严格分析，我们证明随机模型提供了唯一的全局正解。利用李雅普诺夫函数理论创建准则，确保模型在[公式：见原文]处具有唯一的遍历平稳分布。之后，发现了过度噪声可导致霍乱消除的现象。此外，该模型使我们能够研究从过渡到不可预测性的一系列行为，帮助我们从头到尾理解和预测病毒过程。而且，分段微分算子为多个领域的研究人员开辟了新途径，使他们能够在不同时间段传达独特特征。这些算子可以与经典的、卡普托、阿坦加纳 - 巴莱努 - 卡普托分数阶导数以及随机扰动相结合。结果，使用计算建模验证了分析见解，为社会环境中的疾病传播提供了新视角。
