Mean-field approximations for homogeneous networks

Abstract

As seen in Chapters 2 and 3, because of the high-dimensionality of exact mathematical models describing spreading processes on networks, the models are often neither tractable nor numerically solvable for networks of realistic size. We can avoid this fundamental difficulty by refocusing our attention on expected population-scale quantities, such as the expected prevalence or the expected number of edges where one node is susceptible while the other is infectious. This opens up a range of possibilities to formulate so-called mean-field models (i.e. typically low-dimensional ODEs or PDEs) that are widespread in the physics and mathematical biology literature. These are used to approximate stochastic processes, with the potential to be exact in the large system or “thermodynamic” limit, see (for example, [151, 166, 167, 243] and the literature overview in Section 4.8).