Dangerous connections: on binding site models of infectious disease dynamics.
We formulate models for the spread of infection on networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of physiologically structured population models, the formulation starts on the individual level. Influences from the 'outside world' on an individual are captured by environmental variables. These environmental variables are population level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of conditionally independent components: each individual has a fixed number of 'binding sites' for partners. The Markov chain dynamics of binding sites are described by only a few equations. In particular, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population-level quantities are obtained by averaging over individuals in the population. Thus we are able to characterize population-level epidemiological quantities, such as [Formula: see text], r, the final size, and the endemic equilibrium, in terms of the corresponding variables.
Mathematical Institute, Utrecht University, Utrecht, The Netherlands. k.y.leung@uu.nl.|Julius Center for Primary Care and Health Sciences, University Medical Center Utrecht, Utrecht, The Netherlands. k.y.leung@uu.nl.
Ka Yin
0000-0002-7596-7641
KY
Leung
Mathematical Institute, Utrecht University, Utrecht, The Netherlands.
Odo
O
Diekmann
D003141:Communicable Diseases / Q000453:epidemiology*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological
Binding site models; Configuration model; Dynamic networks; Infectious disease dynamics