Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Department of Physical Sciences, The University of Chenab, Gujrat, Pakistan.
Sci Rep. 2024 Sep 10;14(1):21170. doi: 10.1038/s41598-024-70089-z.
Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps.
随机时滞建模对控制传染病的传播动力学具有重要的非药物干预作用，其结果更接近自然的现实。虽然全球已经控制住了新冠疫情，但它仍然存在威胁，并以不同的变体（如奥密克戎和 SARS-CoV-2 等）在全球范围内出现。本文考虑了一种基于易感者、感染者和恢复者群体的数学模型，该模型具有高度非线性的发病率。我们研究了冠状病毒模型的动力学；一个新提出的版本是基于非线性随机时滞微分方程（SDDEs）的随机时滞模型。我们使用转移概率和参数摄动方法来构建随机时滞模型。在一定繁殖数条件下，对模型的正定性、有界性、存在性和唯一性以及平衡点稳定性结果进行了研究。此外，还借助著名的定理研究了疾病的灭绝和持续存在。由于随机时滞微分方程的复杂性，我们使用数值方法来可视化结果。此外，为了进行计算分析，我们实现了文献中现有的方法，并将其结果与所提出的方法（如随机延迟模型的非标准有限差分）进行了比较。该方法可以在自由选择时间步长的情况下恢复模型的所有动力学特性。
