Dissemination models: applications in epidemiology, rumour spreading, wealth distribution, and opinion formation

Abstract

This thesis studies dissemination models across epidemiology, rumour spreading, wealth distribution, and opinion formation, with an emphasis on long-run behaviour and qualitative regimes. Across these settings, we ask when large-scale spread occurs, which long-run behaviours are possible (e.g., extinction, coexistence and oscillations), and how modelling assumptions, such as interaction structure, heterogeneity, and the definition of the diffusing quantity, shape key outcomes. We address these questions using a combination of dynamical-systems methods, matrix/spectral analysis, and Markov-process techniques, supported by numerical computations.