Abboubakar Hamadjam, Banbeto Sylvain Ardo Gouroudja, Jan Rashid, Fandio Rubin, Fouda Henri Paul Ekobena, Khan Ilyas, Khan Muhammad Sabaoon
Department of Computer Engineering, UIT of The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon.
Laboratory of Analysis, Simulation and tests, UIT of The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon.
Sci Rep. 2025 Apr 24;15(1):14245. doi: 10.1038/s41598-025-96887-7.
This study aims to develop and analyze a model of hepatitis B virus transmission dynamics using integer and fractional derivatives in the Caputo sense. After formulating the models, we conduct an asymptotic stability analysis of the disease-free equilibrium point of both models. The Lyapunov technique demonstrates that under specific conditions, the disease-free equilibrium point in both models remains globally asymptotically stable. The study demonstrates that both models can have at least one endemic equilibrium when [Formula: see text], using the vaccination coverage parameter to identify positive equilibrium points. The Banach contraction principle is used to establish the uniqueness and existence of each fractional model's solutions, followed by demonstrating their global stability using the Ulam-Hyers technique. The model is calibrated using reported hepatitis B cases in Nigeria, allowing for parameter estimations. The study indicates that the disease is endemic in this country, as [Formula: see text], indicating a higher level of endemicity. The Adams-Bashforth approach is used to develop a numerical scheme, which is then validated through numerical simulations and evaluated under fractional order parameter variations.
本研究旨在利用Caputo意义下的整数阶和分数阶导数建立并分析乙型肝炎病毒传播动力学模型。在构建模型之后，我们对两个模型的无病平衡点进行了渐近稳定性分析。李雅普诺夫技术表明，在特定条件下，两个模型中的无病平衡点均保持全局渐近稳定。该研究表明，当[公式：见原文]时，两个模型都可以至少有一个地方病平衡点，使用疫苗接种覆盖率参数来确定正平衡点。利用巴拿赫压缩原理建立了每个分数阶模型解的唯一性和存在性，随后使用乌拉姆 - 海尔斯技术证明了它们的全局稳定性。该模型使用尼日利亚报告的乙型肝炎病例进行校准，从而进行参数估计。研究表明，该国该疾病为地方病，因为[公式：见原文]，表明地方病流行程度较高。采用亚当斯 - 巴什福思方法开发了一种数值格式，然后通过数值模拟进行验证，并在分数阶参数变化下进行评估。
