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Applications of the Variance of Final Outbreak Size for Disease Spreading in Networks

Author

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  • Lilia L. Ramírez-Ramírez

    (ITAM)

  • Mary E. Thompson

    (University of Waterloo)

Abstract

The assumption that all susceptible individuals are equally likely to acquire the disease during an outbreak (by direct contact with an infective individual) can be relaxed by bringing into the disease spread model a contact structure between individuals in the population. The structure is a random network or random graph that describes the kind of contacts that can result in transmission. In this paper we use an approach similar to the approaches of Andersson (Ann Appl Probab 8(4):1331–1349, 1998) and Newman (Phys Rev E 66:16128, 2002) to study not only the expected values of final sizes of small outbreaks, but also their variability. Using these first two moments, a probability interval for the outbreak size is suggested based on Chebyshev’s inequality. We examine its utility in results from simulated small outbreaks evolving in simulated random networks. We also revisit and modify two related results from Newman (Phys Rev E 66:16128, 2002) to take into account the important fact that the infectious period of an infected individual is the same from the perspective of all the individual’s contacts. The theory developed in this area can be extended to describe other “infectious” processes such as the spread of rumors, ideas, information, and habits.

Suggested Citation

  • Lilia L. Ramírez-Ramírez & Mary E. Thompson, 2014. "Applications of the Variance of Final Outbreak Size for Disease Spreading in Networks," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 839-862, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9325-z
    DOI: 10.1007/s11009-013-9325-z
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    References listed on IDEAS

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    1. Tom Britton & Theodore Kypraios & Philip D. O'Neill, 2011. "Inference for Epidemics with Three Levels of Mixing: Methodology and Application to a Measles Outbreak," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 578-599, September.
    2. N. Gilbert, 1997. "A Simulation of the Structure of Academic Science," Sociological Research Online, , vol. 2(2), pages 91-105, June.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
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