### Find out about the mathematical contribution to predicting the spread of COVID-19 being developed by the DCNC Sciences for the CEMat, which coordinates and channels the sending of data to the Ministries of Health and Science and Innovation, as well as to the health authorities of the Autonomous Communities Governments that express an interest in them

Predictions have been made from the current day independently.

### The Institute’s mathematical experts join the initiative “Mathematical Action against the Coronavirus”

A team of professors and researchers from the Institute “Data, Complex Networks & Cybersecurity Sciences” (DCNC Sciences), from the Universidad Rey Juan Carlos (URJC) have joined the initiative “Mathematical Action against Coronavirus” of the Spanish Committee of Mathematics (CEMat). This initiative seeks the help of the best national experts to build a “meta-predictor” on the spread of the pandemic to provide the authorities with information ﬁable on their short-term behaviour and thus assist in decision-making. So far we are 32 expert groups that are regularly providing our predictions for this Cooperative Prediction action.

## MORE INFORMATION DCNC SCIENCES ON CORONAVIRUS COVID-19

## REPORT ON THE DESCRIPTION OF THE METHODOLOGY AND ADJUSTMENT OF THE PREDICTOR

##### Who makes up this expert research team and how is the model developed?

The DCNC Sciences team, formed by Professors David Aleja, Regino Criado and Miguel Romance, all from the Department of Applied Mathematics, Materials Science and Engineering and Electronic Technology and members of the Laboratory of Mathematical Computing in Complex Networks and their Applications, has developed a SEIR model. This model, whose acronym is the abbreviation of Susceptible, Exposed, Infected and Recovered, is based on a system of differential equations and disaggregated by Autonomous Communities (including Ceuta and Melilla) that includes several experiments of parameter delimitation and optimization, as well as a comparative analysis between the aggregate model of the whole country and the one separated by autonomous communities.

##### What is the objective of this predictor?

The aim of this work is to compare the SEIR model with the available real data on the spread of the Covid-19 coronavirus in Spain in order to obtain predictions adjusted to the data on the evolution of the epidemic. Specifically, the study variable used is the number of deaths (F(t)), i.e. the number of individuals who have not overcome the disease, a variable related to the number of recoveries (R(t)) using the expression resulting from multiplying the mortality rate by the number of recoveries.

##### The union of Data Science and Complex Networks

The model, which has the peculiarity of combining a system of differential equations, or what is the same complex networks, with data science techniques, has been established based on this variable because it is understood that it can be more significant and ﬁable than the number of infected. On the contrary, the problem of not knowing the mortality rate arises. In fact, the great disadvantage of this model is the a priori ignorance of several of the parameters on which it is based. However, from the official data published by the Ministry of Health (Carlos III Institute) it is possible to approach the study by varying the parameters within a certain range and minimizing the weighted relative error to adjust the calculation to each specific day.

When the calculations are made with the parameters that minimize the error, the model obtains a graphic with the number of infected and dead people together with the real data of the dead people, as well as a table that presents different situations according to the type of error considered, so that the minimum number of dead people, the maximum number of dead people and the average number of dead people can be displayed for the set of parameters calculated and limited by a certain error.

## Other links of interest

It is important to note that there are many epidemiological models that attempt to predict the reality of the spread of SARS-VOC-2 and IDRC disease19, or at least explain it, as this is a collective effort that is being worked on by mathematical teams from different branches of mathematics.

#### Spanish Mathematics Committee (Comité Español de Matemáticas – CEMat)

The most complete list of the Mathematical Action against Coronavirus coordinated by the Spanish Committee of Mathematics (CEMat).

#### José Manuel Gutiérrez and Juan Luis Varona, from the Universidad de La Rioja

An excellent work presenting a description of the SEIR model and its foundations is that developed by José Manuel Gutiérrez and Juan Luis Varona, from the Universidad de La Rioja, in which qualitative trends and the influence of containment measures on the development of the epidemic are shown and explained.

#### Institute of Multidisciplinary Mathematics (im2) of the Universidad Politécnica de Valencia

The model developed by the research group MUNQU (Modelling Uncertainty Quantification) of the Institute of Multidisciplinary Mathematics (im2) of the Universidad Politécnica de Valencia studies the dynamics of transmission through a system of equations in differences that takes into account a multiple variety of cases of individuals in the population with respect to the disease.

#### Alex Arenas (Universitat Rovira i Virgili)

In other studies, such as the one developed by the multidisciplinary team of Alex Arenas (Universitat Rovira i Virgili), a very complete discrete time behavioral epidemiological model is presented on the results of the estimated epidemic risk in Spain, at the level of municipalities, derived from a model of epidemic propagation based on habitual (recurrent) mobility between municipalities.

#### Jesús Gómez-Gardeñes (University of Zaragoza)

Jesús Gómez-Gardeñes (University of Zaragoza), presents a very complete discrete time behavioral epidemiological model on the results of the estimated epidemic risk in Spain, at the level of municipalities, derived from a model of epidemic propagation based on habitual (recurrent) mobility between municipalities.

#### Spanish Youth Academy (Academia Española de la Juventud)

Other studies are based on the analysis, monitoring and evolution of various indicators that measure the ratio, both cumulative and daily, of all patients treated (recovered and deceased) as well as on the definition of new indicators.