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.

The term "herd immunity" is widely used but carries a variety of meanings. Some authors use it to describe the proportion immune among individuals in a population. Others use it with reference to a particular threshold proportion of immune individuals that should lead to a decline in incidence of infection. Still others use it to refer to a pattern of immunity that should protect a population from invasion of a new infection. A common implication of the term is that the risk of infection among susceptible individuals in a population is reduced by the presence and proximity of immune individuals (this is sometimes referred to as "indirect protection" or a "herd effect"). We provide brief historical, epidemiologic, theoretical, and pragmatic public health perspectives on this concept.

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational and spatial scales, which even within a single pathogen often span hours to months, cellular to ecosystem levels, and local to pandemic spread. Some pathogens are directly transmitted between individuals of a single species, while others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity, and dynamic human behavior, raise prevention and control from formerly national to international issues. In the face of this complexity, mathematical models offer essential tools for synthesizing information to understand epidemiological patterns, and for developing the quantitative evidence base for decision-making in global health.

A wide range of communicable human diseases can be considered as spreading through a network of possible transmission routes. The implied network structure is vital in determining disease dynamics, especially when the average number of connections per individual is small as is the case for many sexually transmitted diseases (STDs). Here we develop an intuitive mathematical framework to deal with the heterogeneities implicit within contact networks and those that arise because of the infection process. These models are compared with full stochastic simulations and show excellent agreement across a wide range of parameters. We show how such models can be used to estimate parameters of epidemiological importance, and how they can be extended to examine the effectiveness of various control strategies, in particular screening programs and contact tracing.spatial correlations ͉ pair-wise models ͉ mixing matrix ͉ core groups ͉ contact tracing S exually transmitted diseases (STDs) are an important and increasing public-health problem throughout the world, causing widespread mortality and morbidity and having immense social and economic consequences (1-4). The progress and dynamics of these infections within a population must be understood so that treatment and interventions can be most effectively targeted. Here we present a mechanism to predict the spread of infection through a network of contacts. This work bridges the gap between full simulations, which are difficult to parameterize, and risk-structured mean-field models, which ignore the strong effects attributable to partnerships.The localized spread of infectious diseases has been successfully captured with a variety of spatial models (5-10). Such approaches recognize that the predominantly local nature of disease transmission leads to a high degree of spatial segregation and means that the population is not uniformly well mixed. An alternative and often more realistic strategy is to consider the spread of infection across a network of contacts. This approach is necessary for STDs because proximity in space is no longer the determining risk factor for transmission. The resulting sexual mixing network contains all of the information on potential pathways of infection and as such has proved vital in understanding STD spread (11-18).The sexual mixing network focuses on one of the central issues of epidemiology: who can acquire infection from whom (19)(20)(21)(22). Such networks represent each individual within a population as a node, with connecting edges denoting relationships that could lead to the transmission of infection (Fig. 1). For many of the common airborne infections it may be difficult to define which contacts form an edge (23); for STDs, however, edges are more precisely defined and correspond to sexual partnerships. We note that the network is disease dependent, with STD networks contained within the networks of more readily transmitted infections.The initial spread and long-term behavior of any infectious disease are determined by both its epidemiologi...

Understanding the nature of human contact patterns is crucial for predicting the impact of future pandemics and devising effective control measures. However, few studies provide a quantitative description of the aspects of social interactions that are most relevant to disease transmission. Here, we present the results from a detailed diary-based survey of casual (conversational) and close contact (physical) encounters made by a small peer group of 49 adults who recorded 8661 encounters with 3528 different individuals over 14 non-consecutive days. We find that the stability of interactions depends on the intimacy of contact and social context. Casual contact encounters mostly occur in the workplace and are predominantly irregular, while close contact encounters mostly occur at home or in social situations and tend to be more stable. Simulated epidemics of casual contact transmission involve a large number of non-repeated encounters, and the social network is well captured by a random mixing model. However, the stability of the social network should be taken into account for close contact infections. Our findings have implications for the modelling of human epidemics and planning pandemic control policies based on social distancing methods.