Akram Muhammad, Ihsan Tayyaba
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.
Granul Comput. 2023;8(4):689-707. doi: 10.1007/s41066-022-00349-8. Epub 2022 Sep 26.
Many mathematical models describe the Corona virus disease 2019 (COVID-19) outbreak; however, they require advance mathematical skills. The need for this study is to determine the diffusion of the COVID-19 vaccine in humans. To this end, we first establish a Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy integral transforms to express the effects of COVID-19 vaccination on humans under the generalized Hukuhara partial differential conditions. We extract the analytical solution of the Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy Laplace transform under the generalized Hukuhara partial differential and the Pythagorean fuzzy Fourier transform using the Caputo generalized Hukuhara partial differential. Moreover, we present some essential postulates and results related to the Pythagorean fuzzy Laplace transform and the Pythagorean fuzzy Fourier transform. Furthermore, we develop the solution procedure to extract the solution of the Pythagorean fuzzy partial fractional differential equation. To grasp the considered approach, a mathematical model for the diffusion of the COVID-19 vaccination in the human body is provided and analyzed the behavior to visualize and support the proposed model. Our proposed method is efficient and has a great worth to discuss the bio-mathematical models in various fields of science and medicines.
许多数学模型描述了2019年冠状病毒病（COVID-19）的爆发；然而，它们需要高等数学技能。本研究的目的是确定COVID-19疫苗在人体内的扩散情况。为此，我们首先使用勾股模糊积分变换建立一个勾股模糊偏分数微分方程，以在广义Hukuhara偏微分条件下表达COVID-19疫苗接种对人体的影响。我们在广义Hukuhara偏微分下使用勾股模糊拉普拉斯变换提取勾股模糊偏分数微分方程的解析解，并在Caputo广义Hukuhara偏微分下使用勾股模糊傅里叶变换。此外，我们给出了一些与勾股模糊拉普拉斯变换和勾股模糊傅里叶变换相关的基本假设和结果。此外，我们开发了解决程序以提取勾股模糊偏分数微分方程的解。为了理解所考虑的方法，提供了一个用于COVID-19疫苗接种在人体中扩散的数学模型，并分析了其行为以可视化和支持所提出的模型。我们提出的方法是有效的，对于讨论科学和医学各个领域中的生物数学模型具有很大的价值。
