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Dynamics of stochastic epidemics on heterogeneous networks
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Graham, Matthew (Researcher in complexity science) and House, Thomas A. (2013) Dynamics of stochastic epidemics on heterogeneous networks. Journal of Mathematical Biology, Volume 68 (Number 7). pp. 1583-1605. doi:10.1007/s00285-013-0679-1 ISSN 0303-6812.
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Official URL: http://dx.doi.org/10.1007/s00285-013-0679-1
Abstract
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a heterogeneous network. Using this, we consider analytically the early asymptotic exponential growth phase of such epidemics, showing how the higher order moments of the network degree distribution enter into the stochastic behaviour of the epidemic. We find that the first three moments of the network degree distribution are needed to specify the variance in disease prevalence fully, meaning that the skewness of the degree distribution affects the variance of the prevalence of infection. We compare these asymptotic results to simulation and find a close agreement for city-sized populations.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal of Mathematical Biology | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0303-6812 | ||||||||
Official Date: | 30 April 2013 | ||||||||
Dates: |
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Volume: | Volume 68 | ||||||||
Number: | Number 7 | ||||||||
Page Range: | pp. 1583-1605 | ||||||||
DOI: | 10.1007/s00285-013-0679-1 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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