In order to study the impact of random environments during the spread of the disease, we propose a novel stochastic SIQS model on scale-free networks, which introduces stochastic perturbations to the infected rates. We first obtain the existence of global positive solutions. Moreover, by constructing appropriate stochastic Lyapunov functions, we prove sufficient conditions for extinction and persistence of the disease. Finally, we verify the analysis results through numerical simulations. In addition, the results of previous studies are also improved in our research.

中文翻译：

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无标度网络上随机SIQS流行病模型的动力学行为

为了研究随机环境在疾病传播过程中的影响，我们在无标度网络上提出了一种新颖的随机SIQS模型，该模型将随机扰动引入了感染率。我们首先获得全球积极解决方案的存在。此外，通过构建适当的随机Lyapunov函数，我们证明了该疾病的灭绝和持续存在的充分条件。最后，我们通过数值模拟验证了分析结果。此外，以前的研究结果在我们的研究中也得到了改善。