Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model
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ORIGINAL PAPER
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
Received: 24 April 2020 / Accepted: 5 September 2020 © Springer Nature B.V. 2020
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 (COVID19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R0 is derived. When R0 < 1, the disease-free equilibrium point is unique and locally asymptotically stable. When R0 > 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, quaranThis work is supported by the National Nature Science Foundation of China under Grant 61772063, Beijing Natural Science Foundation under Grant Z180005. C. Xu · Y. Yu · Z. Lu Department of Mathematics ,School of Science, Beijing Jiaotong University, Beijing 100044, China Y. Chen (B) Mechatronics, Embedded Systems and Automation Lab, University of California, Merced, Merced, CA 95343, USA e-mail: [email protected]
tined, 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 · Fractional order · Generalized SEIR model · Epidemic · Peak prediction
1 Introduction The outbreak of the coronavirus disease (COVID-19) in 2019 occurred in Wuhan, China, at the end of 2019. This is a severe respiratory syndrome caused by the novel coronavirus of zoonotic origin [1]. The Chinese government has implemented many measures, including the establishment of specialized hospitals and restrictions on travel, to reduce the spread. By April 20, 2020, the outbreak in China has been basically controlled. However, the outbreak is still rampant all over the world. At present, the USA, Italy, Spain and other countries are still in the rising stage of the outbreak. It has posed a great threat to the public health and safety of the world.
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