#### “We study various scenarios to predict how the end of the lockdown will affect the number of sick and hospitalised people”

#### “Mathematical models can also be applied to improve companies’ production processes”

Mathematical models are sets of equations, functions and formulas that include a set of variables and whose result is a visual representation. They are used to analyse and predict how a system will evolve, from the activity of a group of planets to the evolution of an invasive species in a crop. The UPC research group Computational Biology and Complex Systems Group (BIOCOM-SC), led by Blas Echebarría and directed by Clara Prats in the area of epidemiology, has spent years using mathematical models associated with the evolution of infectious diseases such as malaria, tuberculosis or Chagas. Since the outset of the COVID-19 crisis, the group has used mathematical models to draw up predictive reports on COVID incidence in Catalonia, Spain and the European Union that the authorities are using as one of the references to make decisions.

**What does your COVID 19-related work consist of?**

We prepare a daily analysis of the epidemiological evolution of COVID using data from the European Union, Switzerland, Norway and the United Kingdom. And we make a prediction that was initially from three to five days but has been expanded to a longer period. We make a numerical prediction for five days and a prediction of the final number of sick people. In our analysis, we also include non-European countries such as the USA, Brazil and Peru and the autonomous communities and regions of some countries.

**Who is in the team?**

We are five researchers from BIOCOM-SC and two researchers from the Institute for Health Science Research Germans Trias i Pujol (IGTP). We have also incorporated a dozen Engineering Physics students on placements from the UPC, and we collaborate with researchers from the Institute of Photonic Sciences (ICFO) and the Barcelona Supercomputing Center (BSC).

**How and when did you start to work with mathematical models to analyse the COVID19 pandemic?**

We had already applied mathematical models to other illnesses associated with countries with a low human development index. When the outbreak of COVID19 emerged in China, we analysed the data and studied the curve of cases that were published. We worked to identify the mathematical curve that could reproduce the pattern, and we found the Gompertz function. When the virus reached Europe, we proposed predicting its evolution using this function, and at the start of March we began to generate short-term models.

**Did you do this on your own initiative, or did someone ask you to do it?**

Both things. We started to monitor the situation on our own, but shortly afterwards, through the BSC we received a call from the European Union to ask us to join an international group of modellers. From this point, we started to draw up daily reports that we send to the European Commission, to the European Centre for Disease Prevention and Control (ECDC) and to the Joint Research Centre, and at local level to the Catalan Agency for Health Quality and Evaluation (AQuAS). Through this agency, which is attached to the Catalan Ministry of Health, we are applying the model in Catalonia.

**At this time, are you collaborating with other research groups at international level?**

Yes and no. Many mathematical modelling groups are working on COVID, but the speed of the events does not allow us to function as we would under normal conditions. We are working at such a frenetic pace that it is almost impossible to go outside our research area to look in depth at what others are doing. However, despite the lack of time, we are collaborating we research groups in Brazil and Mexico, and we may start new collaborations in other American and African countries. Our aim is to help facilitate the monitoring of the epidemic in other countries.

**New knowledge will emerge from all of this in the form of scientific output…**

We are already working on papers when we can. What we have found is that everyone is focused on SIR and SEIR models, which are the classic models in epidemiology, but they require information about the disease that is still incomplete and that varies greatly from one country to the next and has a high degree of error. That is why we have focused on data on reported cases, and the model that we use is empirical. Based on experimental points, we analyse the trends using just two parameters. We are gaining better knowledge of the epidemiological situation, establishing the bases of a methodology that can be adapted very quickly to a situation of this type, and generating assessment indicators regarding the risk of an increase in cases and potential lack of control of the disease, among others.

**What two parameters are you using?**

The rate of growth of the disease and the final number of people affected. The Gompertz function is not symmetrical, it grows exponentially at the start and then begins to slow down. One of the parameters refers to how the initial exponential growth decreases and the other indicates the final value the curve reaches, that is, the final number of people affected by COVID19.

**But you handle more data than these…**

Yes, because we do many more things in addition to generating the Gompertz function, which is what we use to draw up the predictions for five days or for the long term. For example, we use the data on deaths to estimate the real number of people infected and so obtain the diagnostic rate for each country, which varies greatly by country. We are also following the hospitalisation curve and the occupation of ICUs, and we use these data to make predictions.

**Have you had to change your way of working?**

It is interesting because our group has almost always worked with mechanistic mathematical models, which are based on knowledge of the system (in this case, about the disease). However, in this situation, what we have seen is that in an emergency in which knowledge of the system (the disease) is very scarce, empirical models are the only way to start to work. COVID 19 has taken us outside our comfort zone.

**You work on this type of models for other infectious diseases associated with developing countries. Did you ever think that the situation would arise in which you had to use the models in an environment closer to home? **

No. We have worked on tuberculosis in Barcelona, and on the flu, with seasonal monitoring, but a lot is known about this disease and we know hardly anything about COVID 19. The truth is that work on the flu has helped us a lot now.

**How do you obtain the data? And how do you manage them?**

Every day, the World Health Organisation and the ECDC publish diagnosed cases and deaths in all the countries that provide information. For the area of hospitalisations, we resort to local databases, so we can regionalise the information for Italy and Spain.

**How do you navigate the problem of varying ways of measuring cases in different territories?**

Countries do not report exactly the same data. We adapt the model to the data provided by each country. If their data collection follows the same pattern, the time series will have certain coherence that our model can reproduce. If there is a change in the methodology for reporting data, the model realises and readjusts, and this is what we do every day.

**Have you considered incorporating another series of non-health data, for example, socioeconomic data, to study the incidence of COVID in different groups or areas?**

Right now it is not possible. But we are assessing mobility data through an agreement with Facebook (Data for Good), which provides information on people’s movement and lockdown indices. The data are provided at provincial level with a degree of detail that does not violate privacy. In the future, anything is possible, we want to be a group that is useful for society.

**Your predictions can be compared days later with real data. What degree of deviation can be seen?**

The percentage of accuracy for one day is above 95%, within the margin of error. In the predictions for five days, the percentage is approximately 75%.

**The measures that the authorities take to slow down the disease have a direct impact on the speed of propagation. Does this appear in the mathematical model that you use?**

We correlate the point at which a control measure is taken with the effect that it produces on the contagion rate. What we have seen is that there are ten days between each political initiative that is taken and its impact. But this does not enable us to make an evaluation, because the reality is much more complex than the mathematics. The context is especially important.

**But could we say that the mathematical models enable us to assess a posteriori the measures that are being taken in the coronavirus crisis?**

At epidemiological level, yes. We can find out the effects that each of the adopted measures has had. But we do not deal with other aspects such as economic or social factors.

**How will the end of lockdown influence the disease incidence?**

It depends on how quickly it is done. If it is done progressively, we will have the ability to react if an index gets out of control. The proper way is to make sure that we can take a step back if necessary. With the ICFO, we are studying different lockdown exit scenarios to predict how the end of lockdown will affect the number of people who are sick and hospitalised, by applying several variables such as the use of masks or the increase in mobility.

**It seems that all of this is making your work more visible…**

Yes. A lot of people are discovering mathematical models because of this, and the use that they can have, their applications. I think that the handling of this crisis without mathematical models would have been a lot worse, without a doubt.

**Thinking of the future, can companies make use of mathematical models to apply them to production processes?**

Definitely. In fact, a few companies have contacted us in the last few weeks. Mathematical models can also be applied to improving production processes in companies.