A Class of Pairwise Models for Epidemic Dynamics on Weighted Networks

Bulletin of Mathematical Biology

Volumn 75, Issue 3, 2013, Pages 466-490

  Rattana, Prapanporn ^a   Blyuss, Konstantin B ^a   Eames, Ken T D ^b   Kiss, Istvan Z ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b LONDON SCHOOL OF HYGIENE AND TROPICAL MEDICINE   (United Kingdom)

Author keywords

Pairwise model; Weighted network

Indexed keywords

EID: 84874116296     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-013-9816-7     Document Type: Article

References (50)

1. Anderson, R. M., & May, R. M. (1992). Infectious diseases of humans. Oxford: Oxford University Press.
2. Ball, F., & Neal, P. (2008). Network epidemic models with two levels of mixing. Math. Biosci., 212, 69-87.
3. Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004a). The architecture of complex weighted networks. Proc. Natl. Acad. Sci. USA, 101, 3747-3752.
4. Barrat, A., Barthélemy, M., & Vespignani, A. (2004b). Weighted evolving networks: coupling topology and weight dynamics. Phys. Rev. Lett., 92, 228701.
5. Barrat, A., Barthélemy, M., & Vespignani, A. (2004c). Modeling the evolution of weighted networks. Phys. Rev. E, 70, 066149.
6. Barrat, A., Barthélemy, M., & Vespignani, A. (2005). The effects of spatial constraints on the evolution of weighted complex networks. J. Stat. Mech., P05003.
7. Beutels, P., Shkedy, Z., Aerts, M., & van Damme, P. (2006). Social mixing patterns for transmission models of close contact infections: exploring self-evaluation and diary-based data collection through a web-based interface. Epidemiol. Infect., 134, 1158-1166.
8. Blyuss, K. B., & Kyrychko, Y. N. (2005). On a basic model of a two-disease epidemic. Appl. Math. Comput., 160, 177-187.
9. Blyuss, K. B., & Kyrychko, Y. N. (2010). Stability and bifurcations in an epidemic model with varying immunity period. Bull. Math. Biol., 72, 490-505.
10. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: structure and dynamics. Phys. Rep., 424, 175-308.
11. Britton, T., Deijfen, M., & Liljeros, F. (2011). A weighted configuration model and inhomogeneous epidemics. J. Stat. Phys., 145, 1368-1384.
12. Britton, T., & Lindenstrand, D. (2012). Inhomogeneous epidemics on weighted networks. Math. Biosci., 260, 124-131.
13. Colizza, V., Barrat, A., Barthélemy, M., Valleron, A.-J., & Vespignani, A. (2007). Modelling the worldwide spread of pandemic influenza: baseline case and containment interventions. PLoS Med., 4, 95-110.
14. Cooper, B. S., Pitman, R. J., Edmunds, W. J., & Gay, N. J. (2006). Delaying the international spread of pandemic influenza. PLoS Med., 3, e212.
15. 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. Interdiscip. Perspect. Infect. Dis., 2011, 284909.
16. Deijfen, M. (2011). Epidemics and vaccination on weighted graphs. Math. Biosci., 232, 57-65.
17. Diekmann, O., & Heesterbeek, J. A. P. (2000). Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Chichester: Wiley.
18. 0, in models for infectious diseases in heterogeneous populations. J. Math. Biol., 28, 365-382.
19. Dorogovtsev, S. N., & Mendes, J. F. F. (2003). Evolution of networks: from biological nets to the Internet and WWW. Oxford: Oxford University Press.
20. Eames, K. T. D. (2008). Modelling disease spread through random and regular contacts in clustered populations. Theor. Popul. Biol., 73, 104-111.
21. Eames, K. T. D., & Keeling, M. J. (2002). Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl. Acad. Sci. USA, 99, 13330-13335.
22. Eames, K. T. D., Read, J. M., & Edmunds, W. J. (2009). Epidemic prediction and control in weighted networks. Epidemics, 1, 70-76.
23. Edmunds, W. J., O'Callaghan, C. J., & Nokes, D. J. (1997). Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections. Proc. R. Soc. Lond. B, Biol. Sci., 264, 949-957.
24. Eubank, S., Guclu, H., Kumar, V. S. A., Marathe, M. V., Srinivasan, A., Toroczkai, Z., & Wang, N. (2004). Modelling disease outbreak in realistic urban social networks. Nature, 429, 180-184.
25. Garlaschelli, D. (2009). The weighted random graph model. New J. Phys., 11, 073005.
26. Gilbert, M., Mitchell, A., Bourn, D., Mawdsley, J., Clifton-Hadley, R., & Wint, W. (2005). Cattle movements and bovine tuberculosis in Great Britain. Nature, 435, 491-496.
27. Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81, 2340-2361.
28. Hatzopoulos, V., Taylor, M., Simon, P. L., & Kiss, I. Z. (2011). Multiple sources and routes of information transmission: implications for epidemic dynamics. Math. Biosci., 231, 197-209.
29. House, T., Davies, G., Danon, L., & Keeling, M. J. (2009). A motif-based approach to network epidemics. Bull. Math. Biol., 71, 1693-1706.
30. House, T., & Keeling, M. J. (2011). Insights from unifying modern approximations to infections on networks. J. R. Soc. Interface, 8, 67-73.
31. Joo, J., & Lebowitz, J. L. (2004). Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation. Phys. Rev. E, 69, 066105.
32. Keeling, M. J. (1999). The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B, Biol. Sci., 266, 859-867.
33. Keeling, M. J., & Eames, K. T. D. (2005). Networks and epidemic models. J. R. Soc. Interface, 2, 295-307.
34. Keeling, M. J., & Rohani, P. (2007). Modeling infectious diseases in humans and animals. Princeton: Princeton University Press.
35. Kiss, I. Z., Green, D. M., & Kao, R. R. (2006). The effect of contact heterogeneity and multiple routes of transmission on final epidemic size. Math. Biosci., 203, 124-136.
36. Kiss, I. Z., Cassell, J., Recker, M., & Simon, P. L. (2010). The impact of information transmission on epidemic outbreaks. Math. Biosci., 225, 1-10.
37. Li, C., & Chen, G. (2004). A comprehensive weighted evolving network model. Physica A, 343, 288-294.
38. Moreno, Y., Pastor-Satorras, R., & Vespignani, A. (2002). Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B, 26, 521-529.
39. Newman, M. E. J. (2002). Spread of epidemic disease on networks. Phys. Rev. E, 66, 016128.
40. Olinky, R., & Stone, L. (2004). Unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission. Phys. Rev. E, 70, 030902(R).
41. Pastor-Satorras, R., & Vespignani, A. (2001a). Epidemic spreading in scale-free networks. Phys. Rev. Lett., 86, 3200-3202.
42. Pastor-Satorras, R., & Vespignani, A. (2001b). Epidemic dynamics and endemic states in complex networks. Phys. Rev. E, 63, 066117.
43. Rand, D. A. (1999). Correlation equations and pair approximations for spatial ecologies. Quart. - Cent. Wiskd. Inform., 12, 329-368.
44. Read, J. M., Eames, K. T. D., & Edmunds, W. J. (2008). Dynamic social networks and the implications for the spread of infectious disease. J. R. Soc. Interface, 5, 1001-1007.
45. Riley, S. (2007). Large-scale spatial-transmission models of infectious disease. Science, 316, 1298-1301.
46. Riley, S., & Ferguson, N. M. (2006). Smallpox transmission and control: spatial dynamics in great Britain. Proc. Natl. Acad. Sci. USA, 103, 12637-12642.
47. Sharkey, K. J., Fernandez, C., Morgan, K. L., Peeler, E., Thrush, M., Turnbull, J. F., & Bowers, R. G. (2006). Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks. J. Math. Biol., 53, 61-85.
48. Wang, S., & Zhang, C. (2004). Weighted competition scale-free network. Phys. Rev. E, 70, 066127.
49. Yang, Z., & Zhou, T. (2012). Epidemic spreading in weighted networks: an edge-based mean-field solution. Phys. Rev. E, 85, 056106.
50. Yang, R., Zhou, T., Xie, Y.-B., Lai, Y.-C., & Wang, B.-H. (2008). Optimal contact process on complex networks. Phys. Rev. E, 78, 066109.