Information diffusion, network overlap and the modelling of epidemics

Many mathematical models of infectious disease spread assume a 'passive' population where individuals' probability of becoming infected and their contact pattern is not altered in any way by the presence of the disease. However, in a realistic scenario, due to the diffusion of the information triggered by the disease, individuals within a population react and can lower their probability of becoming infected. Therefore, disease transmission and the diffusion of information are interlinked and need to be considered simultaneously. In this project, we propose to develop and to analyse a class of novel mathematical and simulation models that allow us to capture the concurrent spread of the disease and information that is generated by the presence of the disease.The project will start by using a simple model formulation in terms of differential equations (i.e. pair-approximation models) to understand and uncover key interactions between the parallel spread of the disease and information. Building on this, we will generalize results for networks of arbitrary size and consider the case when disease and information spread through networks of contacts that are completely overlapping.Using a continuous Markov chain formulation, we will derive analytical results on simple model networks and determine conditions needed to reduce or stop disease transmission. By using network overlap or similarity measures from graph theory, we will adapt and develop custom made overlap measures that are meaningful when disease spread and the diffusion of information are concurrently considered.