Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Türkiye.
Math Biosci Eng. 2022 Jul 21;19(10):10316-10331. doi: 10.3934/mbe.2022482.
In this paper, a novel influenza $ \mathcal{S}\mathcal{I}_N\mathcal{I}_R\mathcal{R} $ model with white noise is investigated. According to the research, white noise has a significant impact on the disease. First, we explain that there is global existence and positivity to the solution. Then we show that the stochastic basic reproduction $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}} {_r} $ is a threshold that determines whether the disease is cured or persists. When the noise intensity is high, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} < 1 $ and the disease goes away; when the white noise intensity is low, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} > 1 $, and a sufficient condition for the existence of a stationary distribution is obtained, which suggests that the disease is still there. However, the main objective of the study is to produce a stochastic analogue of the deterministic model that we analyze using numerical simulations to get views on the infection dynamics in a stochastic environment that we can relate to the deterministic context.
本文研究了一个带有白噪声的新型流感 $ \mathcal{S}\mathcal{I}\mathcal{N}\mathcal{I}\mathcal{R} $ 模型。研究表明，白噪声对疾病有重大影响。首先，我们证明了该模型解的全局存在性和正定性。然后，我们表明随机基本再生数 $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}} {_r} $ 是一个决定疾病是否被治愈或持续存在的阈值。当噪声强度较高时，我们得到 $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} < 1 $，疾病消失；当白噪声强度较低时，我们得到 $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} > 1 $，并得到了存在平稳分布的充分条件，这表明疾病仍然存在。然而，本研究的主要目的是生成确定性模型的随机模拟，我们使用数值模拟对其进行分析，以获得对随机环境下感染动力学的看法，我们可以将其与确定性背景联系起来。
