Norovirus is a contagious disease that causes diarrhea and vomiting and has a significant impact on humanity in terms of medical costs, deaths and mortalities. In this research work, the stochastic modeling techniques are utilized and a novel human norovirus model is investigated keeping in view the contamination of food and water with vaccination effects. It is proved that the model has a unique global solution and by using Lyapunov function theory, sufficient conditions are derived under which the proposed model has a unique ergodic stationary distribution for ${\Re }_{𝔰}^0>1$. It is observed that the disease will extinct out of the population whenever ${\Re }_{𝔰}<1$. To demonstrate the analytical results, two independent examples are depicted graphically by using standard numerical algorithm. To reduce the spread of the virus, we employed certain control measures and an optimal control problem is presented. To further validate the obtained analytical results, additional graphical solutions were generated. This study might provide a robust theoretical framework for a global understanding of chronic communicable illnesses. Our method also aims to provide a method for producing Lyapunov functions, which can be used to explore the stationary distribution of disease models having nonlinear stochastic perturbations.

诺如病毒是一种引起腹泻和呕吐的传染性疾病，在医疗费用、死亡和死亡率方面对人类产生重大影响。在这项研究工作中，利用随机建模技术并研究了一种新型人类诺如病毒模型，同时考虑到食物和水的污染以及疫苗接种效果。证明了该模型具有唯一的全局解，并利用 Lyapunov 函数理论推导了所提出的模型具有唯一的遍历平稳分布的充分条件${\Re }_{𝔰}^0>\mathrm{1个}$. 据观察，该疾病将在任何时候从人口中灭绝${\Re }_{𝔰}<\mathrm{1个}$. 为了证明分析结果，使用标准数值算法以图形方式描述了两个独立的例子。为了减少病毒的传播，我们采用了一定的控制措施，并提出了一个最优控制问题。为了进一步验证获得的分析结果，生成了额外的图形解决方案。这项研究可能为全球理解慢性传染病提供一个强有力的理论框架。我们的方法还旨在提供一种生成 Lyapunov 函数的方法，该函数可用于探索具有非线性随机扰动的疾病模型的平稳分布。