Contact heterogeneity is represented with a metapopulation model.
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We relate the interaction between populations to correlation in disease incidence.
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For two identical populations, this relationship is a simple logistic function.
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The relationship holds for a wide range of parameter values.
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So, case-reporting data alone may be sufficient to infer population interactions.
Abstract
It
is increasingly apparent that heterogeneity in the interaction between
individuals plays an important role in the dynamics, persistence,
evolution and control of infectious diseases. In epidemic modelling two
main forms of heterogeneity are commonly considered: spatial
heterogeneity due to the segregation of populations and heterogeneity in
risk at the same location. The transition from random-mixing to
heterogeneous-mixing models is made by incorporating the interaction, or
coupling, within and between subpopulations. However, such couplings
are difficult to measure explicitly; instead, their action through the
correlations between subpopulations is often all that can be observed.
Here, using moment-closure methodology supported by stochastic
simulation, we investigate how the coupling and resulting correlation
are related. We focus on the simplest case of interactions, two
identical coupled populations, and show that for a wide range of
parameters the correlation between the prevalence of infection takes a
relatively simple form. In particular, the correlation can be
approximated by a logistic function of the between population coupling,
with the free parameter determined analytically from the epidemiological
parameters. These results suggest that detailed case-reporting data
alone may be sufficient to infer the strength of between population
interaction and hence lead to more accurate mathematical descriptions of
infectious disease behaviour.
