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A symbolic investigation of superspreaders. (English) Zbl 1214.92064
Summary: Superspreaders are an important phenomenon in the spread of infectious diseases, accounting for a higher than average number of new infections in the population. We use mathematical models to compare the impact of supershedders and supercontacters on population dynamics. The stochastic, individual based models are investigated by conversion to deterministic, population level mean field equations, using process algebra. The mean emergent population dynamics of the models are shown to be equivalent with and without superspreaders; however, simulations confirm expectations of differences in variability, having implications for individual epidemics.

MSC:
92D30 Epidemiology
60K35 Interacting random processes; statistical mechanics type models; percolation theory
65C20 Probabilistic models, generic numerical methods in probability and statistics
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[1] Anderson, R. M.; May, R. M., Population biology of infectious-diseases. 1, Nature, 280, 361-367 (1979)
[2] Baeten, J. C. M., A brief history of process algebra, Theor. Comput. Sci., 335, 2-3, 131-146 (2005) · Zbl 1080.68072
[3] Bernardo, M.; Degano, P.; Zavattaro, G., Formal methods for computational systems biology (2008), Berlin: Springer, Berlin
[4] Booth, J. (2008). Britain’s Typhoid Marys locked up for life in an Epsom asylum. The Times, 28 July 2008. Available at http://www.timesonline.co.uk/tol/news/uk/health/article4414995.ece (Accessed: 2/2/2010).
[5] Calder, M.; Hillston, J., Process algebra modelling styles for biomolecular processes, Transactions on computational systems biology XI, 1-25 (2009) · Zbl 1260.92030
[6] Cohen, R.; Havlin, S.; ben Avraham, D., Efficient immunization strategies for computer networks and populations, Phys. Rev. Lett., 91, 24 (2003)
[7] Fujie, R.; Odagaki, T., Effects of superspreaders in spread of epidemic, Phys. A Stat. Mech. Appl., 374, 843-852 (2007)
[8] Galvani, A. P.; May, R. M., Epidemiology—dimensions of superspreading, Nature, 438, 7066, 293-295 (2005)
[9] Gibbins, L. N., Mary Mallon: disease denial, and detention, J. Biol. Educ., 32, 127-132 (1998)
[10] Graham, R. L.; Knuth, D. E.; Patashnik, O., Concrete mathematics: a foundation for computer science (1989), Reading: Addison-Wesley, Reading · Zbl 0668.00003
[11] Kemper, J. T., Identification of superspreaders for infectious-disease, Math. Biosci., 48, 111-127 (1980) · Zbl 0442.92024
[12] Kermack, W. O.; McKendrick, A. G., Contributions to the mathematical theory of epidemics i, Proc. R. Soc. Lond. Ser. A, 115, 700-721 (1927) · JFM 53.0517.01
[13] Kurtz, T. G., Solutions of ordinary differential equations as limits of pure jump Markov processes, J. Appl. Probab., 7, 49-58 (1970) · Zbl 0191.47301
[14] Lloyd-Smith, J. O.; Galvani, A. P.; Getz, W. M., Curtailing transmission of severe acute respiratory syndrome within a community and its hospital, Proc. R. Soc. Lond. Ser. B, 270, 1528, 1979-1989 (2003)
[15] Lloyd-Smith, J. O.; Schreiber, S. J.; Kopp, P. E.; Getz, W. M., Superspreading and the effect of individual variation on disease emergence, Nature, 438, 355-359 (2005)
[16] Matthews, L.; Woolhouse, M., New approaches to quantifying the spread of infection, Nat. Rev. Microbiol., 3, 529-536 (2005)
[17] McCaig, C. (2007). From individuals to populations: changing scale in process algebra models of biological systems. Ph.D. thesis, University of Stirling. http://hdl.handle.net/1893/398.
[18] McCaig, C., Norman, R., & Shankland, C. (2008a). Deriving mean field equations from large process algebra models (Technical Report CSM-175). Department of Computing Science and Mathematics, University of Stirling, March 2008. http://hdl.handle.net/1893/1584. · Zbl 1171.92336
[19] McCaig, C.; Norman, R.; Shankland, C., Process algebra models of population dynamics, Algebraic biology, 139-155 (2008), Berlin: Springer, Berlin · Zbl 1171.92336
[20] McCaig, C.; Norman, R.; Shankland, C., From individuals to populations: a symbolic process algebra approach to epidemiology, Math. Comput. Sci., 2, 3, 139-155 (2009) · Zbl 1205.68247
[21] Murata, T., Petri nets: Properties, analysis and applications, Proc. IEEE, 27, 4, 541-580 (1989)
[22] Norman, R.; Shankland, C., Developing the use of process algebra in the derivation and analysis of mathematical models of infectious disease, Computer aided systems theory—EUROCAST 2003, 404-414 (2003), Berlin: Springer, Berlin
[23] Priami, C., Process calculi and life science, Electron. Notes Theor. Comput. Sci., 162, 301-304 (2006)
[24] Tofts, C., Processes with probabilities, priority and time, Form. Asp. Comput., 6, 536-564 (1994) · Zbl 0820.68072
[25] Woolhouse, M. E. J.; Dye, C.; Etard, J. F.; Smith, T.; Charlwood, J. D.; Garnett, G. P.; Hagan, P.; Hii, J. L. K.; Ndhlovu, P. D.; Quinnell, R. J.; Watts, C. H.; Chandiwana, S. K.; Anderson, R. M., Heterogeneities in the transmission of infectious agents: implications for the design of control programs, Proc. Natl. Acad. Sci. USA, 94, 338-342 (1997)
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