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Black, Andrew J.; House, Thomas A.; Keeling, Matthew James; Ross, Joshua V. (2014)
Publisher: Elsevier
Languages: English
Types: Article
Subjects: QA, QR180, R1
Processes that spread through local contact, including outbreaks of infectious diseases, are inherently noisy, and are frequently observed to be far noisier than predicted by standard stochastic models that assume homogeneous mixing. One way to reproduce the observed levels of noise is to introduce significant individual-level heterogeneity with respect to infection processes, such that some individuals are expected to generate more secondary cases than others. Here we consider a population where individuals can be naturally aggregated into clumps (subpopulations) with stronger interaction within clumps than between them. This clumped structure induces significant increases in the noisiness of a spreading process, such as the transmission of infection, despite complete homogeneity at the individual level. Given the ubiquity of such clumped aggregations (such as homes, schools and workplaces for humans or farms for livestock) we suggest this as a plausible explanation for noisiness of many epidemic time series.
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    • Anderson, R. M., Fraser, C., Ghani, A. C., Donnelly, C. A., Riley, S., Ferguson, N. M., Leung, G. M., Lam, T., Hedley, A. J., 2004. Epidemiology, transmission dynamics and control of SARS: the 2002-2003 epidemic. Phil. Trans. R. Soc. Lond. B 359, 1091-1105.
    • Andersson, H., Britton, T., 2000. Stochastic Epidemic Models and Their Statistical Analysis. Vol. 151 of Springer Lectures Notes in Statistics. Springer, Berlin.
    • Ball, F., 1986. A unified approach to the distribtuion of total size and total area under the trajectory of infectives in epidemic models. Adv. App. Prob. 18, 289-310.
    • Ball, F., Donnelly, P., 1995. Strong approximations for epidemic models. Stoch. Proc. Appl 55, 1-21.
    • Ball, F., Mollison, D., Scalia-Tomba, G., 1997. Epidemics with two levels of mixing. Ann. App. Prob. 7 (1), 46-89.
    • Black, A. J., House, T., Keeling, M. J., Ross, J. V., 2013. Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza. J. R. Soc. Interface 10, 20121019.
    • Black, A. J., McKane, A. J., 2011. WKB calculation of an epidemic outbreak distribution. J. Stat. Mech. 12, P12006.
    • Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D., 2006. Complex networks: Structure and dynamics. Physics Reports 424 (4-5), 175-308.
    • Clauset, A., Shalizi, C. R., Newman, M. E. J., 2009. Power-law distributions in empirical data. SIAM Review 51 (4), 661-703.
    • Dangerfield, C. E., Ross, J. V., Keeling, M. J., 2009. Integrating stochasticity and network structure into an epidemic model. J. R. Soc. Interface 6, 761- 774.
    • Danon, L., Ford, A. P., House, T., Jewell, C. P., Keeling, M. J., Roberts, G. O., Ross, J. V., Vernon, M. C., 2011. Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases 2011, 1-28.
    • Ghoshal, G., Sander, L. M., Sokolov, I. M., 2004. SIS epidemics with household structure: the self-consistent field method. Math. Biosci. 190, 71-85.
    • Gilbert, J. A., Meyers, L. A., Galvani, A. P., Townsend, J. P., 2014. Probabilistic uncertainty analysis of epidemiological modeling to guide public health intervention policy. Epidemics, in publication.
    • Graham, M., House, T., 2013. Dynamics of stochastic epidemics on heterogeneous networks. J. Math. Bio., to appear.
    • House, T., Keeling, M. J., 2008. Deterministic epidemic models with explicit household structure. Math. Biosci. 213, 29-39.
    • House, T., Ross, J. V., Sirl, D., 2013. How big is an outbreak likely to be? methods for epidemic final size calculation. Proc. R. Soc. A 469, 20120436.
    • Keeling, M. J., Rohani, P., 2007. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, New Jersey.
    • Kurtz, T., 1970. Solutions of ordinary di erential equations as limits of pure jump Markov processes. J. Appl. Probab. 7 (1), 49-58.
    • Kurtz, T., 1971. Limit theorems for sequences of jump Markov processes approximating ordinary di erential processes. J. Appl. Probab. 8 (2), 344-356.
    • Lloyd, A. L., May, R. M., 1996. Spatial heterogeneity in epidemic models. J. Theor. Biol. 179, 1-11.
    • Lloyd-Smith, J. O., George, D., Pepin, K. M., Pitzer, V. E., Pulliam, J. R., Dobson, A. P., Hudson, P. J., Grenfell, B. T., 2009. Epidemic dynamics at the human-animal interface. Science 326, 1362-1367.
    • Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E., Getz, W. M., 2005. Superspreading and the e ect of individual variation on disease emergence. Nature 438, 255-259.
    • Moler, C., Van Loan, C., 2003. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 20, 801-836.
    • Nerman, O., 1981. On the convergence of supercritical general (C-M-J) branching processes. Z. Wahrscheinlichkeitsch 57, 365-395.
    • Norris, J. R., 1997. Markov chains. Cambridge University Press, Cambridge.
    • Pollett, P., Stefanov, V., 2002. Path integrals for continuous-time Markov chains. J. Appl. Probab. 39, 901-904.
    • Riley, E. C., Murphy, G., Riley, R. L., 1978. Airborne spread of measles in a suburban elementray school. Am. J. Epidemiol. 107, 421-432.
    • Riley, S., et al., 2003. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science 300, 1961- 1966.
    • Ross, J. V., House, T., Keeling, M. J., 2010. Calculation of disease dynamics in a population of households. PLoS ONE 5, e9666.
    • Rozhnova, G., Nunes, A., J., M. A., 2012. Phase lag in epidemics on a network of cities. Phys. Rev. E 85, 051912.
    • Savill, N. J., St Rose, S. G., Keeling, M. J., Woolhouse, M. E. J., 2006. Silent spread of H5N1 in vaccinated poultry. Nature 442, 757.
    • Svensson, A., 2007. A note on generation times in epidemic models. Mathematical Biosciences 208, 300-311.
    • Tildesley, M. J., Savill, N. J., Shaw, D. J., Deardon, R., Brooks, S. P., Woolhouse, M. E. J., Grenfell, B. T., Keeling, M. J., 2006. Optimal reactive vaccination strategies for an outbreak of foot-and-mouth disease in great britain. Nature 440, 83-86.
    • Travers, J., Milgram, S., 1969. An experimental study of the small world problem. Sociometry 32 (4), 425-443.
    • van Kampen, N. G., 1992. Stochastic processes in physics and chemistry. Elsevier, Amsterdam.
    • Wallinga, J., Lipsitch, M., 2007. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. R. Soc. B 274, 599-604.
    • Watts, D. J., Muhamad, R., Medina, D. C., Dodds, P. S., 2005. Multiscale, resurgent epidemics in a hierarchical metapopulation model. Proc. Natl. Acad. Sci. USA 102 (32), 11157-11162.
    • Watts, D. J., Strogatz, S. H., 1998. Collective dynamics of 'small-world' networks. Nature 393, 440-442.
    • Waugh, W. A. O., 1958. Conditioned Markov processes. Biometrika 45, 241- 249.
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