Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India.
Sci Rep. 2024 Feb 20;14(1):4159. doi: 10.1038/s41598-024-54492-0.
The primary goal of the current work is to use a novel technique known as the natural transform decomposition method to approximate an analytical solution for the fractional smoking epidemic model. In the proposed method, fractional derivatives are considered in the Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo senses. An epidemic model is proposed to explain the dynamics of drug use among adults. Smoking is a serious issue everywhere in the world. Notwithstanding the overwhelming evidence against smoking, it is nonetheless a harmful habit that is widespread and accepted in society. The considered nonlinear mathematical model has been successfully used to explain how smoking has changed among people and its effects on public health in a community. The two states of being endemic and disease-free, which are when the disease dies out or persists in a population, have been compared using sensitivity analysis. The proposed technique has been used to solve the model, which consists of five compartmental agents representing various smokers identified, such as potential smokers V, occasional smokers G, smokers T, temporarily quitters O, and permanently quitters W. The results of the suggested method are contrasted with those of existing numerical methods. Finally, some numerical findings that illustrate the tables and figures are shown. The outcomes show that the proposed method is efficient and effective.
目前工作的主要目标是使用一种称为自然变换分解方法的新方法来近似分数吸烟流行模型的解析解。在提出的方法中，在 Caputo、Caputo-Fabrizio 和 Atangana-Baleanu-Caputo 意义上考虑分数导数。提出了一个流行病模型来解释成年人吸毒的动态。吸烟在世界任何地方都是一个严重的问题。尽管有压倒性的证据反对吸烟，但它仍然是一种在社会中广泛存在和被接受的有害习惯。所考虑的非线性数学模型已成功用于解释吸烟在人群中的变化及其对社区公共卫生的影响。使用敏感性分析比较了疾病流行和无疾病两种状态，即疾病在人群中消失或持续存在的状态。已经使用所提出的技术来解决模型，该模型由代表各种已识别吸烟者的五个隔室代理组成，例如潜在吸烟者 V、偶尔吸烟者 G、吸烟者 T、暂时戒烟者 O 和永久戒烟者 W。建议方法的结果与现有数值方法的结果进行了对比。最后，展示了一些说明表格和图形的数值结果。结果表明，所提出的方法是高效和有效的。
