Geodesic
Non-Markovian Stochastic Epidemics in Extremely Heterogeneous Populations
T. House1
1 Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK.
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 153-160

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A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an individual-level non-Markovian stochastic process that converges on standard ODE models of such populations in the appropriate asymptotic limit. A generalised Sellke construction is derived for this model, and this is then used to consider final outcomes in the case where heterogeneity follows a truncated Zipf distribution.
DOI : 10.1051/mmnp/20149210

T. House 1

1 Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. 
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T. House. Non-Markovian Stochastic Epidemics in Extremely Heterogeneous Populations. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 153-160. doi: 10.1051/mmnp/20149210

[1] R. M. Anderson, R. M. May. Infectious Diseases of Humans. Oxford University Press, Oxford, 1991.

[2] H. Andersson, T. Britton. Stochastic Epidemic Models and Their Statistical Analysis, volume 151 of Springer Lectures Notes in Statistics. Springer, Berlin, 2000.

[3] S. Bansal, B. T. Grenfell, L. A. Meyers Journal of the Royal Society Interface 2007 879 91

[4] A. L. Barabási, R. Albert Science 1999 509 512

[5] N. Berger, C. Borgs, J. T. Chayes, A. Saberi. On the spread of viruses on the internet. In Proceedings of the 16th Symposium on Discrete Algorithms, 2005.

[6] R. Pastor-Satorras Physical Review Letters 2010 218701

[7] A. Clauset, C. R. Shalizi, M. E. J. Newman SIAM Review 2009 661 703

[8] L. Danon, A. P. Ford, T. House, C. P. Jewell, M. J. Keeling, G. O. Roberts, J. V. Ross, and M. C. Vernon. Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases, (2011), 1–28.

[9] L. Danon, T. House, M. J. Keeling, J. M. Read Journal of the Royal Society Interface 2012 2826 2833

[10] O. Diekmann, J. A. P. Heesterbeek. Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation. John Wiley Sons Ltd., 2000.

[11] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz Journal of Mathematical Biology 1990 365 382

[12] R. Durrett. Random Graph Dynamics. Cambridge University Press, 2007.

[13] S. Eubank, H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai, N. Wang Nature 2004 180 184

[14] G. R. Grimmett, D. R. Stirzaker. Probability and Random Processes. Oxford University Press, 3rd edition, 2001.

[15] T. House, J. V. Ross, D. Sirl Proceedings of the Royal Society A 2013 20120436

[16] M. J. Keeling, P. Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, New Jersey, 2007.

[17] I. Z. Kiss, D. M. Green, R. R. Kao Mathematical Biosciences 2006 124 36

[18] T. G. Kurtz Journal of Applied Probability 1970 49 58

[19] T. G. Kurtz Journal of Applied Probability 1971 344 356

[20] R. M. May, R. M. Anderson Philosophical Transactions of the Royal Society of London Series B 1988 565 607

[21] R. M. May, A. L. Lloyd Physical Review E 2001 066112

[22] R. Pastor-Satorras, A. Vespignani Physical Review E 2001 066117

[23] R. Pastor-Satorras, A. Vespignani Physical Review E 2002 035108

[24] A. Schneeberger, C. H. Mercer, S. A. J. Gregson, N. M. Ferguson, C. A. Nyamukapa, R. M. Anderson, A. M. Johnson, G. P. Garnett Sexually Transmitted Diseases 2004 380 7

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