critical transition in dynamical systems 30,31. For instance, critical slowing down can precede both first-and second-order transitions 31,32 and is accompanied by the divergence of correlation length in a physical system 33. Many statistics have been used to study EWS in spatially extended systems; temporal 34,35 and spatial correlation 36,37 have been found to precede transitions in spreading processes. Other measurements have been applied to spin systems, where each site in a lattice may be in one of two possible states, possibly partially dependent on the state of neighbouring sites. The spin model has also been applied to opinion dynamics; a simple voter model with binary opinion dynamics is analogous to a physical spin system, where particles represent agents and spins represent different opinions 38. Consensus formation can be seen as a second-order phase transition to an ordered state (where all spins are aligned). In this regime, knowledge of the opinion of a single agent predicts the opinion of all other agents in the system 39. Since the transition in finite networks is smooth 40 , the distance across the network over which the opinions of connected agents are strongly correlated increases smoothly; this is analogous to divergence of the correlation length of a physical system 41. Above some critical temperature, disordered systems take the form of a spin glass. In a spatial opinion model, this describes a state where opinions between neighbours are generally uncorrelated 42. On a static network, this state induces a larger number of edges between dissimilar neighbours as compared to that of consensus regimes. This is related to join count statistics, where the numbers of edges between like neighbours are compared to the number between dislike neighbours as a test of geographical distribution. This is arguably the most natural and well-defined measure for graphs presenting binary data and is used for spatial analysis 43. The necessity of disease surveillance and early warning signals for outbreaks has been discussed in multiple contexts, from epidemic mitigation to bioterrorism prevention 44-46. Potential mitigation of unnecessary expense motivates us to find reliable EWS that remain easily computable on large high-resolution data sets. Furthermore, the study of EWS in coupled disease-behaviour multiplex networks has received relatively little attention, suggesting a significant gap in the literature. Our objective is to evaluate and compare the relative merits of the mutual information, Moran's I, Geary's C and join count statistics as EWS of the occurrence of epidemics and changes in aggregate opinion on a coupled disease-behaviour network model. We use three differently parametrised models (V1, V2 and V3) coupling a binary vaccination opinion dynamic to an SIRV epidemic process. The resulting trends in the EWS for model V2 will be explored in the Results and Discussion sections, with V1 and V3 presented in Supplementary Information S5. The outline of this paper is as follows: the Methods section wil...