Will I get infected or not in a disease epidemic? Should I open a Facebook account or not? Which of the two presidential candidates should I vote for in an American federal election? Under what conditions does my choice or opinion become the popular one? The answer to each of these questions depends not only on the individual in question, but also crucially on their social or physical contacts with other individuals.  University of Limerick researcher, Professor James Gleeson recently published findings in which he has developed a new mathematical technique to predict social phenomena in large populations.  

Professor Gleeson explains: “Contagion can happen in many different contexts, from disease spread to viral marketing. Mathematical modelling is important to help understand the mechanisms that drive contagions on networks. The increasing availability of data from social online networks can now give a lot of information about how humans influence each other, but fast and accurate mathematical techniques are crucial to help process the flood of data”

Understanding human interaction is crucial to formulating social trends. The correct mathematical model can be used to predict a range of scenarios from voting models to infectious disease spread across populations.

Analytical methods for tackling models whether they be voting trends or disease spread are few and often not accurate. Some models can achieve high accuracy but at the cost of computational complexity. In this paper, Professor Gleeson presents a low-complexity approach, called pair approximation, and demonstrates that for certain classes of local decision rules, this formula can achieve results as accurate as the traditional high-complexity approach.  To facilitate the spread of its use, MACSI have made the computational code freely available to download.  

Professor Gleeson is the co-director of the Mathematics Applications Consortium for Science and Industry (MACSI) at the University of Limerick.  This research is funded by Science Foundation Ireland. Professor Gleeson’s paper ‘Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond’   is published in the open-access journal Physical Review X and is available for free download from the American Physical Society.