Effects of control measures on the dynamics of COVID-19 and double-peak behavior in Spain
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ORIGINAL PAPER
Effects of control measures on the dynamics of COVID-19 and double-peak behavior in Spain Jianzhe Huang . Guoyuan Qi
Received: 8 May 2020 / Accepted: 14 August 2020 Ó Springer Nature B.V. 2020
Abstract The COVID-19 disease significantly has threatened the human lives and economy. It is a dynamic system with transmission and control as factors. Modeling the dynamics of the spread of COVID-19 based on the reported data can predict the growing trend of such a disease. In this paper, the dynamic evolution of COVID-19 in Spain is studied, and a comprehensive SEIR model is adopted to fit the obtained clinical progressive data of COVID-19 in Spain. The transmission rate between the susceptible and the self-quarantine susceptible is made to be timevariant, which is reasonable. The equilibria are found, and the stability condition is given using the basic reproduction number and eigenvalues at the points. The effect on daily confirmed cases for the transmission rate from susceptible to the exposed population due to the currently exposed and infectious is extensively investigated. The risk of the easing of the control measure is investigated. The double-peak dynamic behavior of the COVID-19 system is observed. The second wave rebound shows that the
J. Huang School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China G. Qi (&) Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, Tiangong University, Tianjin 300387, China e-mail: [email protected]
daily confirmed cases of the second peak even much higher than the first peak. Keywords COVID-19 Modeling Disease transmission rate Double-peak dynamics
1 Introduction SARS-CoV-2, causing pneumonia and even damaging other parts of the human body, has severely been pandemic in every corner globally. It once had terrible effects in China and has been stabilized in early March 2020. Later, Italy has received great concern due to its number of cumulative confirmed cases and high death ratio [1, 2]. Spain is an adjacent country of Italy; thus, the epidemic situation of COVID-19 in Spain has been dramatically affected, and it even has more cumulative confirmed cases than Italy, according to the report on May 5, 2020 [2]. The transmitting characteristics of COVID-19 and human’s curbing effort have been fighting each other, and the transmission and control as a whole is a dynamic system. Either studying the transmitting degree or investigating human quarantine will fail to find the system mechanism. The priority work is to find a correct dynamic model for COVID-19 in Spain, fitting the available data, and provide a control strategy concerning the spread of the virus. Then it might provide suggestions to suppress the
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J. Huang, G. Qi
spread-out of COVID-19 through studying the dynamic characteristics of such a dynamic model. Backer et al. [3] provided a summary of the estimated incubation period for travelers infected with 2019 novel coronavirus in
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