论文标题
通过广义分数SEIR模型对美国Covid-19的流行趋势的预测分析
Forecast analysis of the epidemics trend of COVID-19 in the United States by a generalized fractional-order SEIR model
论文作者
论文摘要
在本文中，提出了一个广义的分数SEIR模型，该模型由SEIQRP模型表示，该模型具有基本的指导意义，这对于预测可能爆发的传染病爆发（如Covid-19）和其他昆虫疾病具有基本的指导性。首先，分析了模型的某些定性特性。基本复制号$ r_ {0} $是派生的。当$ r_ {0} <1 $时，无病平衡点是独特的，并且在局部渐近稳定。当$ r_ {0}> 1 $时，地方性平衡点也是唯一的。此外，建立了一些条件，以确保无病和地方性平衡点的局部渐近稳定性。预计COVID-19-19的趋势被预测。考虑到个人行为和政府缓解测量的影响，提出了修改后的SEIQRP模型，定义为SEIQRPD模型。根据美国的真实数据，发现我们改进的模型在未来两周内具有更好的预测能力。因此，研究了未来两周美国的流行趋势，并预测了孤立病例的峰值。修改后的SEIQRP模型成功捕获了Covid-19的开发过程，该过程为理解爆发趋势提供了重要的参考。
In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like COVID-19 and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number $R_{0}$ is derived. When $R_{0}<1$, the disease-free equilibrium point is unique and locally asymptotically stable. When $R_{0}>1$, the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the United States is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model. According to the real data of the United States, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the United States in the next two weeks is investigated, and the peak of isolated cases are predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.
