title: From individuals to epidemics.
abstract: Heterogeneous mixing fundamentally changes the dynamics of infectious diseases; finding ways to incorporate it into models represents a critical challenge. Phenomenological approaches are deficient in their lack of attention to underlying process; individual-based models, on the other hand, may obscure the essential interactions in a sea of detail. The challenge then is to find ways to bridge these levels of description, starting from individual-based models and deriving macroscopic descriptions from them that retain essential detail, and filter out the rest. In this paper, attempts to achieve this transformation are described for a class of models where nonrandom mixing arises from the spatial localization of interactions. In general, the epidemic threshold is found to be larger owing to spatial localization than for a homogeneously mixing population. An improved estimate of the dynamics is developed by the use of moment equations, and a simple estimate of the threshold in terms of a 'dyad heuristic'. For more general models in which local infection is not described by mass action, the connection with related partial differential equations is investigated.
authors.affiliation: Department of Ecology and Evolutionary Biology, Princeton University, NJ 08544-1003, USA.
authors.forename: S A
authors.initials: SA
authors.lastname: Levin
authors.forename: R
authors.initials: R
authors.lastname: Durrett
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks; D006801:Humans; D008954:Models, Biological; D011153:Population