Department of Computing, Muscat College, Muscat, Oman.
Chemical Engineering Department, College of Engineering, King Khalid University, 61411, Abha, Saudi Arabia.
Sci Rep. 2022 Sep 27;12(1):16105. doi: 10.1038/s41598-022-20059-0.
In this paper, we propose a mathematical model to describe the influence of the SARS-CoV-2 virus with correlated sources of randomness and with vaccination. The total human population is divided into three groups susceptible, infected, and recovered. Each population group of the model is assumed to be subject to various types of randomness. We develop the correlated stochastic model by considering correlated Brownian motions for the population groups. As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. Once the correlated stochastic model, the existence and uniqueness of a positive solution are discussed to show the problem's feasibility. The SARS-CoV-2 extinction, as well as persistency, are also examined, and sufficient conditions resulted from our investigation. The theoretical results are supported through numerical/graphical findings.
在本文中，我们提出了一个数学模型来描述具有相关性随机源和接种疫苗的 SARS-CoV-2 病毒的影响。总人口被分为易感者、感染者和康复者三组。模型中的每个人群组都假定受到各种类型的随机性的影响。我们通过考虑人群的相关布朗运动来开发相关随机模型。由于环境储层在 SARS-CoV-2 病毒的传播中起着重要作用，我们的模型还包括代表储层的第四个随机微分方程。此外，还考虑了对易感者的接种。一旦建立了相关随机模型，就讨论了正解的存在性和唯一性，以表明该问题的可行性。还研究了 SARS-CoV-2 的灭绝和持续存在，并得出了我们调查的充分条件。理论结果通过数值/图形结果得到支持。
