On global and local critical points of extended contact process on homogeneous trees

Mathematical Biosciences

Volumn 213, Issue 1, 2008, Pages 13-17

  Sugimine, Nobuaki ^a,d   Masuda, Naoki ^a,b   Konno, Norio ^c   Aihara, Kazuyuki ^a,d  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^b RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^c YOKOHAMA NATIONAL UNIVERSITY   (Japan)

^d INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

Author keywords

Global and local critical points; Households models

Indexed keywords

BIOTECHNOLOGY; GRAPH THEORY; STOCHASTIC MODELS;

CRITICAL INFECTION RATE; GLOBAL AND LOCAL CRITICAL POINTS; HOUSEHOLDS MODELS;

EPIDEMIOLOGY;

CRITICAL ANALYSIS; DISEASE INCIDENCE; EPIDEMIC; HOUSEHOLD STRUCTURE; INFECTIOUS DISEASE; STOCHASTICITY;

ARTICLE; EPIDEMIC; GLOBAL CHANGE; HOUSEHOLD; INFECTION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; TREE;

COMMUNICABLE DISEASES; DISEASE OUTBREAKS; EPIDEMIOLOGIC METHODS; FAMILY CHARACTERISTICS; HUMANS; MODELS, STATISTICAL; STOCHASTIC PROCESSES;

EID: 42649134108     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2008.02.004     Document Type: Article

References (20)

1. Ball F.G. Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Math. Biosci. 156 (1999) 41
2. * and secure vaccination coverage. Biometrika 91 (2004) 345
3. Ball F.G., Britton T., and Lyne O.D. Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes. Math. Biosci. 191 (2004) 19
4. Ball F.G., and Lyne O.D. Stochastic multitype SIR epidemics among a population partitioned into households. Adv. Appl. Probab. 33 (2001) 99
5. Ball F.G., and Lyne O.D. Optimal vaccination policies for stochastic epidemics among a population of households. Math. Biosci. 177-178 (2002) 333
6. Durrett R. Lecture Notes on Particle Systems and Percolation (1988), Wadsworth, Belmont, CA
7. Harris T.E. Contact interactions on a lattice. Ann. Probab. 2 (1974) 969
8. Jensen I., and Dickman R. Time-dependent perturbation theory for diffusive non-equilibrium lattice models. J. Phys. A: Math. Gen. 26 (1993) L151
9. In: Koch C., and Segev I. (Eds). Methods in Neuronal Modeling. second ed. (1998), The MIT Press, A Bradford Book, Cambridge
10. Konno N. Phase Transitions of Interacting Particle Systems (1994), World Scientific Press, Singapore
11. Konno N., Schinazi R., and Tanemura H. Coexistence results for a spatial stochastic epidemic model. Markov Process. Relat. Fields 10 (2004) 367
12. Krone S. The two-stage contact process. Ann. Appl. Probab. 9 (1999) 331
13. Liggett T.M. Interacting Particle Systems (1985), Springer, New York
14. Liggett T.M. Improved upper bounds for the contact process critical value. Ann. Probab. 23 (1995) 697
15. Liggett T.M. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (1999), Springer, New York
16. Masuda N., Konno N., and Aihara K. Transmission of severe acute respiratory syndrome in dynamical small-world networks. Phys. Rev. E 69 (2004) 031917
17. Schinazi R. On the importance of risky behavior in the transmission of sexually transmitted diseases. Math. Biosci. 173 (2001) 25
18. Schinazi R. On the role of social clusters in the transmission of infectious diseases. Theor. Popul. Biol. 61 (2002) 163
19. Schonmann R.H. Multiplicity of phase transitions and mean-field criticality on highly non-amenable graphs. Commun. Math. Phys. 219 (2001) 271
20. Sudbury A.W. Rigorous lower bounds for the critical birth-rate in the diffusive contact process. J. Appl. Probab. 38 (2001) 1074