European and US lockdowns and second waves during the COVID-19 pandemic

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This paper investigates the lockdowns to contain the spread of the SARS-CoV-2 coronavirus in France, Germany, Italy, Spain, the UK and the US and also recent developments since these lockdowns have been relaxed. The analysis employs a two-stage SEIR model with different reproductive numbers pre- and post-lockdown. These parameters are estimated from data on the daily number of confirmed cases in a process that automatically detects the time at which the lockdown became effective. The model is evaluated by considering its predictive accuracy on current data and is then extended to a three-stage version to explore relaxations. The results show the extent to which each country was successful in reducing the reproductive number and demonstrate how the approach is able to model recent increases in the number of cases in all six countries, including the second peak in the US. The results also indicate that the current levels of relaxation in all five European countries could lead to significant second waves that last longer than the corresponding first waves. While there is uncertainty about the implications of these findings at this stage, they do suggest that a lot of vigilance is needed.
Original languageEnglish
Article number108472
Number of pages13
JournalMathematical Biosciences
Early online date24 Sept 2020
Publication statusPublished (in print/issue) - 31 Dec 2020


  • Coronavirus
  • lockdowns
  • relaxation
  • second wave
  • two-stage SEIR model
  • predictive accuracy


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