A versatile ODE approximation to a network model for the spread of sexually transmitted diseases |
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Authors: | Bauch C T |
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Institution: | (1) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. e-mail: bauch@math.mcmaster.ca, CA |
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Abstract: | We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a
steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application
to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been
attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic
and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population
of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular
network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error
of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations.
We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic.
Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range
of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure
approximation is very flexible in the kinds of network models it can approximate.
Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002
C.T.B. was supported by the NSF.
Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership
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