Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a 'mixing network'. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. Therefore, characteristics of mixing networks-and how these deviate from the random-mixing norm-have become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures.Here, we review the basis of epidemiological theory (based on random-mixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.

Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time.

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large-scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a ¢xed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.

Summary Fundamental ecological research is both intrinsically interesting and provides the basic knowledge required to answer applied questions of importance to the management of the natural world. The 100th anniversary of the British Ecological Society in 2013 is an opportune moment to reflect on the current status of ecology as a science and look forward to high‐light priorities for future work. To do this, we identified 100 important questions of fundamental importance in pure ecology. We elicited questions from ecologists working across a wide range of systems and disciplines. The 754 questions submitted (listed in the online appendix) from 388 participants were narrowed down to the final 100 through a process of discussion, rewording and repeated rounds of voting. This was done during a two‐day workshop and thereafter. The questions reflect many of the important current conceptual and technical pre‐occupations of ecology. For example, many questions concerned the dynamics of environmental change and complex ecosystem interactions, as well as the interaction between ecology and evolution. The questions reveal a dynamic science with novel subfields emerging. For example, a group of questions was dedicated to disease and micro‐organisms and another on human impacts and global change reflecting the emergence of new subdisciplines that would not have been foreseen a few decades ago. The list also contained a number of questions that have perplexed ecologists for decades and are still seen as crucial to answer, such as the link between population dynamics and life‐history evolution. Synthesis. These 100 questions identified reflect the state of ecology today. Using them as an agenda for further research would lead to a substantial enhancement in understanding of the discipline, with practical relevance for the conservation of biodiversity and ecosystem function.

BackgroundMathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models.Methods and FindingsFirst, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options.ConclusionThis work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks.