SEIR modeling of the COVID-19 and its dynamics
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ORIGINAL PAPER
SEIR modeling of the COVID-19 and its dynamics Shaobo He . Yuexi Peng
. Kehui Sun
Received: 25 April 2020 / Accepted: 4 June 2020 Ó Springer Nature B.V. 2020
Abstract In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input. Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system. We found that the parameters of the proposed SEIR model are different for different scenarios. Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation. Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system. Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model. Keywords COVID-19 Coronavirus SEIR model Nonlinear dynamics Control
S. He Y. Peng (&) K. Sun School of Physics and Electronics, Central South University, Changsha 410083, China e-mail: [email protected]
1 Introduction At the end of 2019, a novel coronavirus disease (COVID-19) was declared as a major health hazard by World Health Organization (WHO). At present, this disease is rapidly growing in many countries, and the global number of COVID-19 cases is increasing at a rapid rate. This coronavirus is a kind of enveloped, single stranded and positive sense virus which belongs to the RNA coronaviridae family [1, 2]. In early December of 2019, this infectious disease has begun to outbreak in Wuhan, the capital city of Hubei province, China. Until now, the epidemic in China is basically under control, but there are still many infections around the world. To defeat the epidemic, scientists in different fields investigated the COVID-19 from different points of view. Those aspects include pathology, sociology perspective, the infection mechanism and prediction [3–8]. In the history of mankind, there are many other outbreak and transmission of diseases such as dengue fever, malaria, influenza, pestilence and HIV/AIDS. How to built a proper epidemiological model for these epidemics is a challenging task. Some scientists treat the disease spread as a complex network for forecast and modeling [9, 10]. For the COVID-19, Bastian Prasse et al. [10] designed a network-based model which is built by the cities and traffic flow to describe the epidemic in the Hubei province. At present, the SIS [11, 12], SIR[13] and SEIR [14, 15] models provide
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another way for the simulation of epidemics. Lots of research works have been reported. It shows that those SIS, SIR and SEIR models can reflect the dynamics of different epidemics well. Meanwhile, these models have been used to model the COVID-19 [16, 17]. For instance, Tang et al. [17] investigated a general SEIRtype epidemiolog
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