Viewing Trends in Graph Connectivity as Early Warnings of Epidemics and Vaccine Crises

When measles was rampant, suffering apparent, and relief desired, the prospect of vaccination was received with open arms by a grateful public. But it worked \emph{too} well, and opinions slowly diverged; scientists saw aggregate health as proof of the efficacy of intervention, while some of the lay public wondered "But do we really need this vaccine, though? I don't see sick people..." Spurious 1998 research linking the MMR vaccine to autism was published and our dreams of eradication evaporated; the diseases were back to stay. The spread of vaccine disinformation through social networks is immediately apparent and easily exploited, even more so due to the strong assortativity of social networks (both online and face-to-face). Therein lies the focus of this thesis; we investigate different measures of spatial grouping as early warnings signals (EWS) of epidemics through the simulation of social and contact networks and the use of various statistical and graph theoretical tools. Using an agent-based model coupling a binary voting dynamic with an SIRVp model of infection, we simulate a vaccine preventable disease. Each week, agents are given the opportunity to change opinion to that of a friend, while having potentially disease-spreading interactions with many people. The first study confirms that changes in trend of the Moran's I, Geary's C and mutual information statistics give early warnings of the critical transitions representing both vaccine crises and epidemics. This is independent of the strength of an injunctive social norm, though through change point testing we confirm that these warnings come closer to vaccine crises as the norm becomes stronger. We find also that the observable distance between vaccine crisis and epidemic spread decreases as the norm strengthens. Confirmation of these results for other different models boosts our confidence in our results. Our second study shows that graph theoretical changes in incidences of opinion-based communities and echo chambers coincide reliably with outbreaks. Clustering, network modularity and the rate of opinion change also provide EWS of both vaccine crises and epidemics in the population. Due to the immense size and traffic of current social networks, only portions of interactions can be observed at any one time, and therefore our third study tests previously effective signals against an incorporation of vaccine hesitance and network sampling. We find that these identified tools remain good EWS, though experiencing penalties on effectiveness dependent on the sampling rate of the population. In sum, our work provides easily employable tools to predict important negative epidemiological events using readily available data, the best-performing of which is the entropy-based mutual information statistic. Given current and expected events, we believe that this thesis makes a solid contribution to the sparse EWS literature for coupled disease-behaviour systems, as well as providing tools that can be used to inform policy decisions surrounding the mitigation of human folly and critical infection events