Alshammari Nawa A, Alharthi N S, Mohammed Saeed Abdulkafi, Khan Adnan, Ganie Abdul Hamid
Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Saudi Arabia.
Department of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh, Saudi Arabia.
PLoS One. 2025 May 28;20(5):e0321089. doi: 10.1371/journal.pone.0321089. eCollection 2025.
Measles is a highly contagious illness that can spread throughout a population based on the number of susceptible or infected individuals as well as their social dynamics within the society. The measles epidemic is thought to be controlled for the suffering population using the susceptible-exposed-infectious-recovered (SEIR) epidemic model, which depicts the direct transmission of infectious diseases. To better explain the measles epidemics, we provided a nonlinear time fractional model of the disease. The solution of SEIR is obtained by using the Caputo fractional derivative operator of order [Formula: see text]. The Homotopy perturbation transform method (HPTM) and Yang transform decomposition methodology (YTDM) have been employed to obtain the numerical solution of the time fractional model. Obtaining numerical findings in the form of a fast-convergent series significantly improves the proposed techniques accuracy. The behaviour of the approximate series solution for several fractional orders is shown graphically which are derived through Maple. A graphic representation of the behaviours of susceptible, exposed, infected, and recovered individuals are shown at different fractional order values. Figures that depict the behaviour of the projected model are used to illustrate the developed results. Finally, the present work may help you predict the behaviour of the real-world models in the wild class with respect to the model parameters. It was found that the majority of patients who receive therapy join the recovered class when various epidemiological classes were simulated at the effect of fractional parameter [Formula: see text]. These approaches shows to be one of the most efficient methods to solve epidemic models and control infectious diseases.
麻疹是一种极具传染性的疾病，它能够在人群中传播，其传播情况取决于易感个体或感染个体的数量以及他们在社会中的社交动态。麻疹疫情被认为可以通过易感-暴露-感染-康复（SEIR）疫情模型来控制受影响人群，该模型描述了传染病的直接传播。为了更好地解释麻疹疫情，我们提供了该疾病的非线性时间分数模型。SEIR的解是通过使用阶数为[公式：见原文]的Caputo分数导数算子获得的。同伦摄动变换方法（HPTM）和杨变换分解方法（YTDM）已被用于获得时间分数模型的数值解。以快速收敛级数的形式获得数值结果显著提高了所提出技术的准确性。通过Maple得出了几个分数阶的近似级数解的行为，并以图形方式展示。展示了易感、暴露、感染和康复个体在不同分数阶值下行为的图形表示。描绘预测模型行为的图形用于说明所得到的结果。最后，本研究可能有助于你预测野生类现实世界模型相对于模型参数的行为。研究发现，当在分数参数[公式：见原文]的影响下模拟各种流行病学时，大多数接受治疗的患者会进入康复类别。这些方法被证明是解决疫情模型和控制传染病的最有效方法之一。
