The Covid-19 outbreak in Spain. A simple dynamics model, some lessons, and a theoretical framework for control response.

Spain is among the countries worst hit by the Covid-19 pandemic, with one of the highest rate of infections and deaths per million inhabitants. First positive was reported on late January 2020. Mid March, with 7,000 confirmed cases, nationwide lockdown was imposed. Mid May the epidemic was stabilized and government eased measures. Here we model the dynamics of the epidemic in Spain over the whole span, and study the effectiveness of control measures. The model is also applied to Italy and Germany. We propose formulas to easily estimate the size of the outbreak and the benefit of early intervention. A susceptible-infectious-recovered (SIR) model was used to simulate the epidemic. The growth and transmission rates, doubling time, and reproductive number were estimated by least-mean-square fitting of daily cases. Time-series data were obtained from official government reports. We forecasted the epidemic curve after lockdown under different effectiveness scenarios, and nowcasted the trend by moving average sliding window. Exponential growth expressions were derived. Outbreak progression remained under the early growth dynamics. The basic reproductive number in Spain was 2.5 ± 0.1 (95% CI 2.3-2.7), and the doubling time was 2.8 ± 0.1 days (95% CI 2.6-3.0). Slight variations in measures effectiveness produce a large divergence in the epidemic size. The effectiveness in Spain was 68%, above control threshold (60%). During lockdown the reproductive number dropped to an average of 0.81 ± 0.02 (95% CI 0.77-0.85). Estimated epidemic size is about 300,000 cases. A 7-days advance of measures yields a reduction to 38%. The dynamics in Spain is similar to other countries. Strong lockdown measures must be adopted if not compensated by rapid detection and isolation of patients, and even a slight relaxation would raise the reproductive number above 1. Simple calculations allow anticipating the size of the epidemic based on when measures are taken and their effectiveness. Spain acted late. Control measures must be implemented immediately in the face on an epidemic.