In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (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 USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, 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 USA in the next two weeks is investigated, and the peak of isolated cases is 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.

本文提出了一种广义分数阶SEIR模型，记为SEIQRP模型，将人群分为易感者、暴露者、传染者、隔离者、康复者和不感者，对预测可能发生的疫情具有基本的指导意义。传染病，如 2019 年冠状病毒病 (COVID-19) 和未来的其他昆虫疾病。首先，分析了模型的一些定性特性。推导出基本再生数\({{ R }}_{0}\) 。当\({{ R }}_{0}<1\)时，无病平衡点唯一且局部渐近稳定。当\({{ R }}_{0}>1\)时，地方性平衡点也是唯一的。此外，还建立了一些条件来确保无病平衡点和地方病平衡点的局部渐近稳定性。预测了 COVID-19 在美国的传播趋势。考虑到个人行为和政府缓解措施的影响，提出了改进的SEIQRP模型，定义为SEIQRPD模型，将人群分为易感个体、暴露个体、传染个体、隔离个体、康复个体、不受影响个体和死亡个体。根据美国的真实数据，发现我们改进的模型对未来两周的疫情趋势有更好的预测能力。因此，我们对美国未来两周的疫情趋势进行了调查，并预测了孤立病例的高峰。修改后的SEIQRP模型成功捕捉了COVID-19的发展过程，为了解疫情趋势提供了重要参考。