Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model

Conghui Xu; Yongguang Yu; YangQuan Chen; Zhenzhen Lu

doi:10.1007/s11071-020-05946-3

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model

Nonlinear Dyn. 2020;101(3):1621-1634. doi: 10.1007/s11071-020-05946-3. Epub 2020 Sep 14.

Authors

Conghui Xu¹, Yongguang Yu¹, YangQuan Chen², Zhenzhen Lu¹

Affiliations

¹ Department of Mathematics ,School of Science, Beijing Jiaotong University, Beijing, 100044 China.
² Mechatronics, Embedded Systems and Automation Lab, University of California, Merced, Merced, CA 95343 USA.

Abstract

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.

Keywords: COVID-19; Epidemic; Fractional order; Generalized SEIR model; Peak prediction.