Transmission is the driving force in the dynamics of any infectious disease. A crucial element in understanding disease dynamics, therefore, is the 'transmission term' describing the rate at which susceptible hosts are 'converted' into infected hosts by their contact with infectious material. Recently, the conventional form of this term has been increasingly questioned, and new terminologies and conventions have been proposed. Here, therefore, we review the derivation of transmission terms, explain the basis of confusion, and provide clarification. The root of the problem has been a failure to include explicit consideration of the area occupied by a host population, alongside both the number of infectious hosts and their density within the population. We argue that the terms 'density-dependent transmission' and 'frequency-dependent transmission' remain valid and useful (though a 'fuller' transmission term for the former is identified), but that the terms 'mass action', 'true mass action' and 'pseudo mass action' are all unhelpful and should be dropped. Also, contrary to what has often been assumed, the distinction between homogeneous and heterogeneous mixing in a host population is orthogonal to the distinction between density- and frequency-dependent transmission modes.

Many pathogens and parasites attack multiple host species, so their ability to invade a host community can depend on host community composition. We present a graphical isocline framework for studying disease establishment in systems with two host species, based on treating host species as resources. The isocline approach provides a natural generalization to multi‐host systems of two related concepts in disease ecology – the basic reproductive rate of a parasite, and threshold host density. Qualitative isocline shape characterizes the threshold community configurations that permit parasite establishment. In general, isocline shape reflects the relative forces of inter‐ and intraspecific transmission of shared parasites. We discuss the qualitative implications of parasite isocline shape for issues of mounting concern in conservation ecology.

Simulation studies using susceptible-infectious-recovered models were conducted to estimate individuals' risk of infection and time to infection in small-world and randomly mixing networks. Infection transmitted more rapidly but ultimately resulted in fewer infected individuals in the small-world, compared with the random, network. The ability of measures of network centrality to identify high-risk individuals was also assessed. "Centrality" describes an individual's position in a population; numerous parameters are available to assess this attribute. Here, the authors use the centrality measures degree (number of contacts), random-walk betweenness (a measure of the proportion of times an individual lies on the path between other individuals), shortest-path betweenness (the proportion of times an individual lies on the shortest path between other individuals), and farness (the sum of the number of steps between an individual and all other individuals). Each was associated with time to infection and risk of infection in the simulated outbreaks. In the networks examined, degree (which is the most readily measured) was at least as good as other network parameters in predicting risk of infection. Identification of more central individuals in populations may be used to inform surveillance and infection control strategies.

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