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A semiempirical model, based in the logistic map, was developed to forecast the different phases of the COVID-19 epidemic. This paper shows the mathematical model and a proposal for its calibration. Specific results are shown for Spain. Four phases were considered: non-controlled evolution; total lock-down; partial easing of the lock-down; and a phased lock-down easing. For no control the model predicted the infection of a 25% of the Spanish population, 1 million would need intensive care and 700,000 direct deaths. For total lock-down the model predicted 194,000 symptomatic infected, 85,700 hospitalized, 8600 patients needing an Intensive Care Unit (ICU) and 19,500 deaths. The peak was predicted between the 29 March/3 April. For the third phase, with a daily rate r=1.03, the model predicted 400,000 infections and 46,000±15,000 deaths. The real r was below 1%, and a revision with updated parameters provided a prediction of 250,000 infected and 29,000±15,000 deaths. The reported values by the end of May were 282,870 infected and 28,552 deaths. After easing of the lock-down the model predicted that the health system would not saturate if r was kept below 1.02. This model provided good accuracy during epidemics development.

Application of a Semi-Empirical Dynamic Model to Forecast the Propagation of the COVID-19 Epidemics in Spain