Endemic infections are always possible on regular networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 88, Issue 4, 2013, Pages

  Del Genio, Charo I ^a,b,c   House, Thomas ^a,b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL APPROACH; CLUSTERING COEFFICIENT; NETWORK STRUCTURES; NUMERICAL RESULTS; REGULAR NETWORKS;

CONDENSED MATTER PHYSICS;

PHYSICS;

ARTICLE; COMMUNICABLE DISEASE; DISEASE TRANSMISSION; ENDEMIC DISEASE; THEORETICAL MODEL;

COMMUNICABLE DISEASES; ENDEMIC DISEASES; MODELS, THEORETICAL;

EID: 84886661836     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.040801     Document Type: Article

References (46)

1. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
2. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.10.009 424, 175 (2006).
3. L. Danon, A. P. Ford, T. House, C. P. Jewell, M. J. Keeling, G. O. Roberts, J. V. Ross, and M. C. Vernon, Interdiscip. Perspect. Infect. Dis. 10.1155/2011/284909 2011, 284909 (2011).
4. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3200 86, 3200 (2001).
5. M. D. F. Shirley and S. P. Rushton, Ecol. Complex. 1476-945X 10.1016/j.ecocom.2005.04.005 2, 287 (2005).
6. M. Lelarge, in SIGMETRICS '09: Proceedings of the Eleventh International Joint Conference on Measurement and Modeling of Computer Systems (ACM, New York, 2009).
7. S. A. Levin and R. Durrett, Philos. Trans. R. Soc., B PTRBAE 0962-8436 10.1098/rstb.1996.0145 351, 1615 (1996);
8. R. Durrett and D. Remenik, Ann. Appl. Probab. 1050-5164 10.1214/08-AAP581 19, 1656 (2009);
9. R. Durrett, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0914402107 107, 4491 (2010).
10. M. J. Keeling, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rspb.1999.0716 266, 859 (1999);
11. T. House and M. J. Keeling, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2010.12.009 272, 1 (2011).
12. O. Givan, N. Schwartz, A. Cygelberg, and L. Stone, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2011.07.015 288, 21 (2011).
13. M. A. Abdullah, C. Cooper, and M. Draief, in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, edited by, L. A. Goldberg, K. Jansen, R. Ravi, and, J. D. P. Rolim, (Springer, Berlin, 2011), p. 351.
14. M. J. Keeling and C. A. Gilligan, Nature (London) NATUAS 0028-0836 10.1038/35038073 407, 903 (2000).
15. N. M. Ferguson, C. A. Donnelly, and R. M. Anderson, Science SCIEAS 0036-8075 10.1126/science.1061020 292, 1155 (2001).
16. G. J. Gibson, Phytopathology PHYTAJ 0031-949X 10.1094/PHYTO.1997.87.2.139 87, 139 (1997).
17. C. I. Del Genio, T. Gross, and K. E. Bassler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.178701 107, 178701 (2011).
18. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
19. M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003);
20. M. E. J. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 103.058701 103, 058701 (2009);
21. Networks: An Introduction (Oxford University Press, Oxford, UK, 2010).
22. E. Volz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.056115 70, 056115 (2004).
23. J. P. Gleeson and S. Melnik, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.046121 80, 046121 (2009).
24. B. Bollobás, S. Janson, and O. Riordan, Random Struct. Algorithms 1042-9832 10.1002/rsa.20322 38, 269 (2011).
25. T. Britton, M. Deijfen, A. N. Lagerås, and M. Lindholm, J. Appl. Probab. JPRBAM 0021-9002 10.1239/jap/1222441827 45, 743 (2008);
26. F. Ball, D. Sirl, and P. Trapman, Math. Biosci. MABIAR 0025-5564 10.1016/j.mbs.2009.12.003 224, 53 (2010);
27. F. Ball, T. Britton, and D. Sirl, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s00285-012-0609-7 66, 979 (2013).
28. M. Moslonka-Lefebvre, M. Pautasso, and M. J. Jeger, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2009.06.015 260, 402 (2009).
29. C. Molina and L. Stone, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2012.08.036 315, 110 (2012).
30. J. G. Kirkwood and E. M. Boggs, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1723737 10, 394 (1942).
31. M. Á. Serrano and M. Boguñá, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.088701 97, 088701 (2006).
32. P. Trapman, Math. Biosci. MABIAR 0025-5564 10.1016/j.mbs.2007.05.011 210, 464 (2007).
33. K. Satō, H. Matsuda and A. Sasaki, J. Math. Biol. JMBLAJ 0303-6812 10.1007/BF00163881 32, 251 (1994).
34. C. J. Rhodes and R. M. Anderson, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.1996.0088 180, 125 (1996).
35. A. Kleczkowski, C. A. Gilligan, and D. J. Bailey, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rspb.1997.0135 264, 979 (1997).
36. J. A. N. Filipe and G. J. Gibson, Philos. Trans. R. Soc., B PTRBAE 0962-8436 10.1098/rstb.1998.0354 353, 2153 (1998);
37. J. A. N. Filipe and M. M. Maule, Math. Biosci. MABIAR 0025-5564 10.1016/S0025-5564(02)00224-9 183, 15 (2003).
38. S. P. Ellner, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.2001.2322 210, 435 (2001).
39. J. L. Payne and M. J. Eppstein, Evol. Comput. 1063-6560 10.1162/evco.2009.17.2.203 17, 203 (2009).
40. P. Grassberger, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(82) 90036-0 63, 157 (1983).
41. L. M. Sander, Math. Biosci. MABIAR 0025-5564 10.1016/S0025-5564(02)00117- 7 180, 293 (2002).
42. C. I. Del Genio, H. Kim, Z. Toroczkai, and K. E. Bassler, PLoS One 1932-6203 10.1371/journal.pone.0010012 5, e10012 (2010).
43. H. Kim, C. I. Del Genio, K. E. Bassler, and Z. Toroczkai, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/14/2/023012 14, 023012 (2012).
44. M. Molloy and B. Reed, Random Struct. Algorithms 1042-9832 10.1002/rsa.3240060204 6, 161 (1995).
45. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968).
46. M. Tidlesley, T. House, M. Bruhn, R. Curry, M. O'Neill, G. Smith, and M. J. Keeling, Proc. Natl. Acad. Sci. USA 107, 3 (2010).