大众传播渠道干预和隔离策略下COVID-19动态的高级和综合研究：确定性和概率方法
Advanced and comprehensive research on the dynamics of COVID-19 under mass communication outlets intervention and quarantine strategy: a deterministic and probabilistic approach
摘要：
持续的2019冠状病毒病（COVID-19）是一场重大危机，对医疗保健行业和全球经济产生了重大影响，这使其成为科学和技术研究各个领域的主要课题。为了正确理解和控制这种新的流行病，数学建模是一个非常有效的工具，可以说明其传播的机制。在这方面，使用房室模型是文献中采用的描述COVID-19动态的最主要方法。沿着同样的路线，我们的目标是在这项研究中，概括和改善许多现有的作品，奉献给分析这种流行病的行为。准确地说，我们提出了一个针对冠状病毒的SQEAIHR流行病系统。我们构建的模型是丰富的，考虑到媒体的干预和重要的动态。通过使用下一代矩阵方法，获得了COVID-19的理论基本再生数$R_0$。基于一些非标准的和广义的分析技巧，证明了当$R_0 < 1$ .而且，在$R_0 > 1$的情况下，也显示了COVID-19模型的一致持久性。为了使模型更符合实际情况，通过考虑比例白噪声，将随机性因素考虑在内，得到了一个适定性的随机模型.在适当的条件下，证明了有趣的渐近性质，即：灭绝和持久的平均。理论结果表明，扰动COVID-19模型的动力学由与随机噪声大小密切相关的参数决定。最后，我们提出了一些数值例子来证实我们的理论结果，并显示媒体干预和隔离策略的影响。
英文摘要：
The ongoing Coronavirus disease 2019 (COVID-19) is a major crisis that has significantly affected the healthcare sector and global economies, which made it the main subject of various fields in scientific and technical research. To properly understand and control this new epidemic, mathematical modelling is presented as a very effective tool that can illustrate the mechanisms of its propagation. In this regard, the use of compartmental models is the most prominent approach adopted in the literature to describe the dynamics of COVID-19. Along the same line, we aim during this study to generalize and ameliorate many existing works that consecrated to analyse the behaviour of this epidemic. Precisely, we propose an SQEAIHR epidemic system for Coronavirus. Our constructed model is enriched by taking into account the media intervention and vital dynamics. By the use of the next-generation matrix method, the theoretical basic reproductive number $R_0$ is obtained for COVID-19. Based on some nonstandard and generalized analytical techniques, the local and global stability of the disease-free equilibrium are proven when $R_0 < 1$. Moreover, in the case of $R_0 > 1$, the uniform persistence of COVID-19 model is also shown. In order to better adapt our epidemic model to reality, the randomness factor is taken into account by considering a proportional white noises, which leads to a well-posed stochastic model. Under appropriate conditions, interesting asymptotic properties are proved, namely: extinction and persistence in the mean. The theoretical results show that the dynamics of the perturbed COVID-19 model are determined by parameters that are closely related to the magnitude of the stochastic noise. Finally, we present some numerical illustrations to confirm our theoretical results and to show the impact of media intervention and quarantine strategies.
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