Journal of Mathematical Biology

, Volume 68, Issue 7, pp 1583–1605 | Cite as

Dynamics of stochastic epidemics on heterogeneous networks



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.


SIR model Diffusion Transmission Networks 

Mathematics Subject Classification

92D30 90B15 



The authors would like to acknowledge the financial support received from EPSRC, the editor and two anonymous reviews for their helpful comments, in particular relating to the analyses presented in Sect. 3.3 and Appendix C


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Complexity ScienceUniversity of WarwickCoventryUK
  2. 2.Warwick Mathematics InstituteUniversity of WarwickCoventryUK

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