Effects of control measures on the dynamics of COVID-19 and double-peak behavior in Spain

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 time-variant, 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 daily confirmed cases of the second peak even much higher than the first peak.