Mathematics vs. social models: how to understand the sociology of corona virus spread

by Prof. Dr. Frank Dignum, Umeå University

This week we been able to contribute to the discussion of the usefulness of track and trace apps in the Netherlands. Our results show that by themselves these apps have none or minimal effect on the spread of the virus. Besides all legal, constitutional and ethical issues, their use may lead to a false feeling of security which ultimately can contribute to a second wave of the contagion. Other studies, based on large scale mathematical models of epidemics show the opposite effect. I.e. according to those studies, track and trace apps do have a positive effect on the containment of the virus. It is important to compare these types of studies and see why they lead to different results. Even if I do not know all studies, I’ve been discussing this subject with several researchers.
I hope that in the coming weeks I will have time to write a scientific paper describing the arguments very precisely mathematically and scientifically. In this blog, I will try to explain the issue in a more informal and easy to follow way. The major difference between our model and those used by many epidemiologists is that we have a simulation based on human behavior which we use together with the epidemiological model. That is, we use the same mathematical model for spreading the virus as epidemiologists use. That’s something the epidemiologists don’t expect because we have such different results.
The crux for the difference between ours and their models, lies in a number of specific properties of the corona virus:

• Firstly, the time between becoming infected and possibly showing symptoms is quite long. So people can infect others unnoticed for quite some time. In an epidemiological model, this is translated by giving a parameter a different value. However, if we now look at how many interactions people have and with which other people, you can use a kind of probabilistic model in a mathematical model that divides the interactions uniformly or normally over all possibilities. That differs somewhat from reality if the interval in which this happens is short, but not so much that it disturbs the results a lot. However, if that interval becomes longer, the mathematical model is no longer correct. We see this often in macroeconomic models: they do reasonably well in normal situations, but in crisis situations people do not behave according to expectations and the deviations are too great to make those models even of value.
• Another issue is the skewed age distribution of the corona virus infection: relatively many young people are asymptomatic. So they are infected without knowing it and spread (with lower chance, but still) the virus. Because they are not being tested, this distribution continues. Young people also meet more other young people on average, so the contagion can go on for quite some time before being noticed. From the perspective of the track and trace apps, this means that people have already fallen from the contact list that is about a week long. In this way, there are a lot of points along which the virus still spreads despite the use of the app.
• Demographics and living arrangements are also a determining factor. Last Friday we developed a simulation about the use of apps in Italy. People’s lives there look a little different than in the Netherlands. So the results are slightly different, but the conclusion remains. In the Italian case, the positive effect of testing randomly 20% of the population is even greater than in the Netherlands.

The issues above are not easy to capture in macro level models, as those used in epidemiology. Macro models consider individuals to be mostly behaving in a similar way and aggregate across large population numbers. It is difficult for this models to identify pockets of specific, different, behaviors. It is similar to say that everybody in the Netherlands is 42,6 years because that is the median age for the whole Dutch population. So, our models consider the differences between people’s ages, backgrounds, living situation and behavioral motives. In this way, we can identify the possible differences across the population and how things like the track and trace apps can be expected to be used given the characteristics of a specific group.

Many scientific studies point out that the lack of a human behavior model in the epidemic models is a problem, but this is not so well known among the general public. So far, very little has been done on this issue. Our team is one of the few in the world that combines the human models with the epidemic models. It would be nice if a lot more research was done, because then this type of models would improve greatly and there would be more comparative studies.