Jonathan Ward (University of Leeds) – Mean-field approximation of epidemic dynamics on networks

Many biological and social systems can be modelled as dynamical processes on networks. An important example are epidemics, where vertices in the network represent people, edges indicate social contacts and the dynamic describes how people’s health (susceptible to infection, infected, recovered etc.) changes in time in response to the health of the people they come into contact with. Biological models based on chemical reaction networks can also be described as dynamics on networks when there is network structure that governs which units can interact, and consequently the law of mass action no longer holds. These examples, and others, can be described exactly as Markov chains, but typically there are too many states for this to be of practical use. Thus it is standard to derive "mean-field" approximations, although this is often done using probabilistic intuition. In this talk I will describe a robust method to approximate a class of dynamical processes on networks based on an explicit average of their exact Markov chain description. While this provides a systematic method to derive mean-field approximations, it remains an open challenge to quantify the error introduced.