Covid-19 in Spain



These prognosis techniques can also be used to study how a pandemic like Covid-19 develops and help planning ahead.

They allow us to act in order to reduce the number of people infected and try to reduce the deceased. The Agents have to decide how to face a pandemic and one of the biggest concerns is how the data is analyzed, in particular, how the mortality rate is worked out only taking into account the total confirmed number of deceased and the number of diagnosed cases. These calculations result in much higher mortality rates, creating a great public alarm. The most reliable data that can be accessed are the number of dead, the number of patients admitted in hospital and patients in intensive care, all provided by the Spanish Government. How is the virus spreading in Spain? How are the different regional governments performing? Can the different health systems be coordinated to reduce the number of dead and make better use of resources?

In order to reduce uncertainty, different models were considered in the analysis here presented, and it was concluded that the spread of Covid-19 follows the Verhulst equation, a logistic function developed in 1938. This model would help the system take preventive actions and act in a coordinated manner, making use of the resources available in the different regions.

As the data becoming available increases, they can be used to adjust more sophisticated models. The Verlhurst model is a particular case of the general growth equation that is derived fixing two parameters. Other possible model of 4 parameters are Bertalanffy and Richards. In fact, the analysis of many locations allowed us to realize that the tiem since the confinent measurements are taken until the number of deaths reaches cero is about 2-3 months. For that reason, even though some parameters might not be statistically significant we are always fitting Bertalanffy and Richards model, because it allows to reach cero deaths in periods about 2-3 moths. In fact the main reason why parameters are not statistically significant is the noise and errors contained in data.

It is important to emphasize that the source of the data used is the website It has been identified that some regions have changed the way they manage their data, which can obviously influence the results of the model. However, even if the real number of dead was greater than the published data, this would affect the estimate of deceased but not so much the attenuation sequence with time. 

From this moment on, and given the controversy caused by data management, we will accurately describe the additional study that we have carried out trying to shed some light into this issue. The motivation, in addition to the controversy of the data arises from the difficulties we are having in adjusting the data to the 4-parameter model, especially considering that when applyed to other countries, such as Great Britain or states, such as New York, the adjustment is outstanding. For this reason we have downloaded the data from the system for the Surveillance of daily mortality from all causes in Spain (MOMO), with these data we have used the following procedure:

  1. We check excess mortality with respect to the 99% confidence bands, to eliminate all those who can be deceased due to natural causes with a probability of 99%.
  2. We compared this excess mortality with the official data of deaths from COVID-19 (
  3. If the excess is greater than the official COVID figure, we assume that those killed by COVID-19 actually correspond to all those killed above that 99% quantile, and we discard the official figure.
  4. If the excess is less, we maintain the official figure.

The results are shown in the graphs, where we include the official and estimated data using the MOMO data and our methodology. Coincidence or not, now we do that many of the models are statistically significant. With this process, in the communities with the most deceased, the official figures skew the peaks, with which the numbers of deceased and future estimates increase (Note: The official data that appears at the national level do not contain the figures for Catalonia, because They have been temporarily removed for correction. However, we include the deceased in Catalonia according to MOMO). As expected, the time sequence of death mitigation does not appear to be altered, i.e. confinement is really working.

Note 1: The virus mortality rate has been updated in accordance with the data from coronavirus-age-sex-demographics and the Spanish population pyramid at different regions (INE), and therefore the estimate of number of cases improves. In addition we consider an uncertainty for each death rate of 1%.

Note 2: It has been decided to remove the model with hospital admissions. The fact that the admissions and discharges are provided in a cumulative manner, makes the data not useful when feeding the model. Figures of admissions and discharges of both hospitals and intensive care units would be required.

Note 3: We have carried out a comparative analysis of the situation in Spain, Italy and China that we have found interesting. We have made it available to the working group Acción Matemática contra el Coronavirus but it is still an analysis carried out by us, with our own interpretation of the data. (Download the report)

Note 4: Below the map we also include a ranking based on estimates of final number of deaths per million inhabitants. Note that positions might change according to the improvement in final estimates.

Note 5: Due to the effort involved in the daily update of the approximately 275 models that we processed with the new information available, we have decided to stop updating it, not without first writing a final reflection on what we have learned during the process of modeling of the COVID-19, which by the way, constitutes the first entry of our recently released blog.

If someone is especially interested in an specific location, please contact us through our web, indicating both the location from which you would like to have updates and a brief explanation of the usefulness of the information we offer. We will be happy to update that specific location.

COVID-19 evolution during first wave


Since December 14th, the European Centre for Disease Prevention and Control stopped providing daily information and started giving it on a weekly basis. Since we get Spanish data from ECDPC we have adapted current graphs to the weekly information, including data from MOMO database.