Skip to main content
Article thumbnail
Location of Repository

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

By Frank G. Ball, David J. Sirl and Pieter Trapman


This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored

Publisher: Elsevier
Year: 2010
OAI identifier:
Provided by: Nottingham ePrints

Suggested articles


  1. (1995). A critical point for random graphs with a given degree sequence,
  2. (2002). A general model for stochastic SIR epidemics with two levels of mixing, doi
  3. (1990). A nonstandard family of polynomials and the final size distribution of Reed-Frost epidemic processes,
  4. (1986). A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models, doi
  5. (1971). An introduction to probability theory and its applications. doi
  6. An SIR epidemic model on a random network with household structure,
  7. (2008). Analytical results for bond percolation and k-core sizes on clustered networks, doi
  8. (1998). Effect of variability in infection period on the persistence and spatial spread of infectious diseases, doi
  9. (1999). Epidemic models and social networks,
  10. (2008). Epidemics on random graphs with tunable clustering,
  11. (1997). Epidemics with two levels of mixing, doi
  12. (2008). Network epidemic models with two levels of mixing,
  13. (2005). Network theory and SARS: predicting outbreak diversity, doi
  14. On a certain model of an epidemic,
  15. (2007). On analytical approaches to epidemics on networks, doi
  16. (1980). Oscillatory phenomena in a model of infectious diseases, doi
  17. (2004). Probability: theory and examples, 2nd Edition, doi
  18. (2006). Random graph dynamics, doi
  19. (1995). Reproduction numbers and critical immunity levels for epidemics in a community of households, in:
  20. Reproductive numbers, epidemic spread and control in a community of households,
  21. (2007). Second look at the spread of epidemics on networks, doi
  22. (2002). Spread of epidemic disease on networks, doi
  23. (2000). Stochastic epidemic models and their statistical analysis,
  24. (2001). Stochastic multitype SIR epidemics among a population partitioned into households, doi
  25. (2000). Susceptibility sets and the final outcome of stochastic SIR epidemic models,
  26. (1986). Symmetric sampling procedures, general epidemic processes and their threshold limit theorems,
  27. (1978). The asymptotic number of labeled graphs with given degree sequences,
  28. (1999). The distribution of general final state random variables for stochastic epidemic models, doi
  29. (1967). The distribution of the total size of an epidemic, in:
  30. (2006). The effect of contact heterogeneity and multiple routes of transmission on final epidemic size, doi
  31. (1995). The effect of household distribution on transmission and control of highly infectious diseases, doi
  32. (2008). The relationship between real-time and discretegeneration models of epidemic spread,
  33. (1982). The spatial general epidemic and locally dependent random graphs, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.