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The great circle epidemic model

Author

Listed:
  • Ball, Frank
  • Neal, Peter

Abstract

We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n-->[infinity] is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n-->[infinity] by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution.

Suggested Citation

  • Ball, Frank & Neal, Peter, 2003. "The great circle epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 233-268, October.
    • Handle: RePEc:eee:spapps:v:107:y:2003:i:2:p:233-268
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    References listed on IDEAS

    as
    1. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    2. Ball, Frank & Donnelly, Peter, 1995. "Strong approximations for epidemic models," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 1-21, January.
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