Mean-field approximation of dynamics on networks

Speaker's Name: Jonathan Ward
Speaker's Affiliation: University of Leeds
Speaker's Research Theme(s): Applied Mathematics
Abstract:
Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. In this talk I will describe how such systems are typically studied using stochastic simulations and mean-field approximations. While mean-field approximations are a widely used tool, they are typically derived using plausible probabilistic reasoning, introducing uncontrolled errors that may lead to invalid mathematical conclusions. I will show how mean-field approximations can be derived from an exact description of Markov chain dynamics on networks through a process of averaging called approximate lumping. This approach provides a general framework for the derivation of mean-field approximations of dynamics on networks that unifies previously disconnected methods and highlights the sources of error.

Venue: UP-Maths A17