Bounding basic characteristics of spatial epidemics with a new percolation model

Advances in Applied Probability

Volumn 43, Issue 2, 2011, Pages 335-347

  Meester, Ronald ^a   Pieter, Trapman ^a,b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

Dependent percolation; Epidemics

Indexed keywords

BOND PERCOLATION; DEPENDENT PERCOLATION; EPIDEMICS; GENERAL MODEL; LOCALLY FINITE GRAPH; OPEN-PATH; PERCOLATION MODELS; PERCOLATION PROBABILITY; RANDOM WEIGHT;

EPIDEMIOLOGY; PERCOLATION (SOLID STATE); SOLVENTS;

GRAPH THEORY;

EID: 79960053351     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1308662482     Document Type: Article

References (21)

1. Andersson, H. (1999). Epidemic models and social networks. Math. Scientist. 24, 128-147.
2. Andersson, H. and Britton, T. (2000). Stochastic Epidemic Models and Their Statistical Analysis. (Lecture Notes Statist. 151), Springer, NewYork.
3. Balister, P., Bollobás, B. and Walters, M. (2005). Continuum percolation with steps in the square or the disk. Random Structures Algorithms 26, 392-403. (Pubitemid 41053998)
4. Becker, N. G. and Starczak, D. N. (1998). The effect of random vaccine response on the vaccination coverage required to prevent epidemics. Math. Biosci. 154, 117-135. (Pubitemid 29056972)
5. Becker, N. G. and Utev, S. (2002). Protective vaccine efficacy when vaccine response is random. Biom. J. 44, 29-42.
6. Bollobás, B., Janson, S. and Riordan, O. (2007). The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31, 3-122.
7. Britton, T., Deijfen, M. and Martin-Löf, A. (2006). Generating simple random graphs with prescribed degree distribution. J. Statist. Phys. 124, 1377-1397. (Pubitemid 44581233)
8. Chayes, L. and Schonmann, R. H. (2000). Mixed percolation as a bridge between site and bond percolation. Ann. Appl. Prob. 10, 1182-1196. (Pubitemid 33246405)
9. Chung, F. and Lu, L. (2002), Connected components in random graphs with given expected degree sequences. Ann. Combinatorics 6, 125-145.
10. Cox, J. T. and Durrett, R. (1988). Limit theorems for the spread of epidemics and forest fires. Stoch. Process. Appl. 30, 171-191.
11. Diekmann, O. and Heesterbeek, J. A. P. (2000). Mathematical Epidemiology of Infectious Diseases. John Wiley, Chichester.
12. Grimmett, G. (1999). Percolation, 2nd edn. Springer, Berlin.
13. Jagers, P. (1975). Branching Processes with Biological Applications. JohnWiley, London.
14. Kenah, E. and Robins, J. M. (2007). Second look at the spread of epidemics on networks. Phys. Rev. E 76, 036113, 12pp.
15. Kuulasmaa, K. (1982). The spatial general epidemic and locally dependent random graphs. J. Appl. Prob. 19, 745-758.
16. Miller, J. C. (2008). Bounding the size and probability of epidemics on networks. J. Appl. Prob. 45, 498-512.
17. Newman, M. E. J. (2002). Spread of epidemic disease on networks. Phys. Rev. E 66, 016128, 11pp.
18. Norros, I. and Reittu, H. (2006). On a conditionally Poissonian graph process. Adv. Appl. Prob. 38, 59-75.
19. Trapman, P. (2007). On analytical approaches to epidemics on networks. Theoret. Pop. Biol. 71, 160-173. (Pubitemid 46186472)
20. Watts, C. H. and May, R. M. (1992). The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math. Biosci. 108, 89-104.
21. Wierman, J. C. (1994). Substitution method critical probability bounds for the square lattice site percolation model. Combinatorics Prob. Comput. 4, 181-188.