Covid-19 in the world

CASE STUDY:

COVID-19 IN THE WORLD

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 country governments. How is the virus spreading in the world? How are the different 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 https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide. 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. We are working on this, trying to correct these possible effects and investigating the sources and how the data is managed by each country.

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

Note 2: 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 in spanish)

Note 3: 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 4: 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.

 

Select a country on the map to see COVID-19 evolution