A Social-Physics Approach to Modeling and Analyzing Epidemics

Tanimoto, Jun

This chapter presents the background and motivation for why this book came about. Needless to say, this book has two key words besides “sociophysics,” and these are “evolutionary game” and “mathematical epidemiology.” Game theory is a contemporary mathematical concept founded in the middle of the twentieth century by the milestone work of John von Neumann and Oskar Morgenstern; “Theory of Games and Economic Behavior” (Princeton University Press, 1944). Following their work, John Nash played an important role in applying the theory to various domains, including economics, information science, and biology; for his efforts, he was awarded the Nobel Prize in Economics in 1994 due to his establishment of the concept of Nash Equilibrium. Briefly, game theory can be described as a mathematical template for modeling human decision-making processes. If one intends to address the time-evolutionary aspect of a dynamical system, this is called evolutionary game theory (EGT), as distinct from classic game theory, which focuses on a static situation in which several game players with several strategies mutually interact to maximize their benefits (called a “payoff”) at a certain moment. After the concept of complex science emerged in the 1990s and computational resources surged, EGT was combined with multi-agent simulation (MAS) to open up a new horizon through which it is possible to approach many complex problems related to human social systems that contain physical systems as subordinates. Such problems had previously been considered unsolvable because human behavior was seen as too stochastic to appropriately predict the dynamics of decision-making. A disease spreading in our society is a good example. Epidemiology—meaning the study of how an epidemic spreads on a human network—can be said to be sufficiently predictable because we know that it obeys a simple physics: the principle of diffusion phenomena. But the behavior of each individual is so varied, so prone to stochastic deviation, and so significantly influenced by information from the media that it is hard to predict how a disease will really spread through a complex human social system. In fact, whether one commits to pre-emptive vaccination or not is deeply related to the costs of the illness and the vaccination, and is also significantly influenced by the extent of the current outbreak as it stochastically evolves in time. This is quite a difficult task: but this book aims to address it in the following chapters.