Rafique Mudassar, Rehamn Muhammad Aziz Ur, Alqahtani Aisha M, Rafiq Muhammad, Aljohani A F, Iqbal Zafar, Ahmed Nauman, Niazai Shafiullah, Khan Ilyas
Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia.
Sci Rep. 2025 Jan 30;15(1):3784. doi: 10.1038/s41598-025-87385-x.
This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in place of integer order derivatives and including the delay factors in the susceptible and infectious compartments. Moreover, unique existence of the solution for the underlying model is ensured by establishing some benchmark results. Likewise, the positivity and boundedness of the solutions for the projected model is explored. The basic reproduction number is [Formula: see text] is found out for the model. The time-delayed non-integer order STID model holds two steady states, namely, the STID free and endemic steady state. The model stability is carried out at the steady states. The non-standard finite difference (NSFD) technique is hybridized with the Grunwald Letnikov (GL) approximation for finding the numerical solutions of the time-delayed non-integer order STID model. The boundedness and non-negativity of the numerical scheme is confirmed. The simulated graphs are presented with the help of an appropriate test example. These graphs show that the proposed numerical algorithm provides the positive bounded solutions. The article is ended with productive outcomes of the study.
本研究旨在调查性传播感染疾病（STID）的动态情况，这是一个严重的健康问题。在此过程中，通过引入Caputo分数阶导数取代整数阶导数，并在易感和感染 compartments 中纳入延迟因素，将整数阶STID模型推进到时滞非整数阶STID模型。此外，通过建立一些基准结果确保了基础模型解的唯一存在性。同样，还探讨了投影模型解的正性和有界性。求出了该模型的基本再生数为[公式：见原文]。时滞非整数阶STID模型有两个稳态，即无STID稳态和地方病稳态。在稳态处进行了模型稳定性分析。将非标准有限差分（NSFD）技术与Grunwald Letnikov（GL）近似相结合，以求解时滞非整数阶STID模型的数值解。证实了数值格式的有界性和非负性。借助一个适当的测试示例给出了模拟图。这些图表明所提出的数值算法提供了正的有界解。文章以该研究的丰硕成果结束。
