HQ Team
January 24, 2025: A recent study led by Empa researchers has developed a new mathematical model that improves predictions of how fast an epidemic spreads by utilizing the friendship paradox, a phenomenon first identified by sociologist Scott Feld in 1991. This model, which incorporates a reproduction matrix rather than a single reproduction number (R), offers a more nuanced understanding of how diseases spread through social networks.
Friendship Paradox
The friendship paradox elucidates that an individual’s friends tend to have more friends than they do themselves. This observation stems from the fact that well-connected individuals are more likely to be included in others’ social circles. For instance, in a study analyzing Facebook data, users averaged 190 friends while their friends averaged 635, demonstrating the paradox’s prevalence across social networks.
Ivan Lunati, head of the Computational Engineering laboratory, and the research team recognized that during an epidemic, people with many contacts—often referred to as superspreaders—play a crucial role in spreading infections. Traditional models assume that each infectious person infects an average number of others. This number is referred to as the reproduction number (R). If R is greater than one, the number of cases increases exponentially; if R is less than one, it decreases. However, this approach fails to account for the diminishing number of potential hosts as the epidemic progresses. The new model addresses this limitation by considering how different population groups interact and become infected at varying rates.
Reproduction matrix
Lunati and his associates, therefore, propose the use of the reproduction matrix, which takes into account the heterogeneity of the contacts. “We wanted to go beyond the simplified interpretation of the reproduction number R and better capture the complexity of real epidemic waves,” says Hossein Gorji, part of the research group. “The reproduction matrix allows us to predict the spread of disease more accurately by taking into account both the non-linearity and heterogeneity that are often overlooked in conventional models.”
Using COVID-19 data from Switzerland and Scotland, the researchers demonstrated that their reproduction matrix could predict infection peaks more accurately than conventional models. They found that early in an outbreak, superspreaders drive case numbers up rapidly, but as these individuals become infected, the rate of new infections declines more quickly than traditional models would suggest.
Lunati’s research indicates that the average number of contacts varies significantly with age; individuals aged 10 to 25 typically have the most connections. This age-based grouping helps refine predictions but also highlights the complexity of social interactions. Explains Lunati. “In addition, our model assumes that the superspreaders as well as the number of cases are evenly distributed throughout the country. This assumption is not very problematic for small countries, with strongly interconnected regions and relatively uniform social structures. For large countries, however, we would also have to take into account the geographical distribution of the population and the contacts between the regions.”
The implications of this research extend beyond infectious diseases. The reproduction matrix can be applied to various contexts where networks are involved, such as the spread of ideas or behaviors within society. Future work aims to explore how this model can simulate the adoption of new technologies or sustainable practices among different demographic groups.
Lunati and his team’s innovative approach opens avenues for applying network theory to broader societal challenges.
