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Volumn 205, Issue 1, 2007, Pages 59-76

Convergence results for contact branching processes

Author keywords

Asymptotic speed of translation; Convergence in probability; Epidemic link; Multi type contact branching process

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; PROBABILITY DISTRIBUTIONS;

EID: 33845220522     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.05.001     Document Type: Article
Times cited : (1)

References (24)
  • 1
    • 0242446784 scopus 로고    scopus 로고
    • Mathematical challenges in spatial ecology
    • Neuhauser C. Mathematical challenges in spatial ecology. Notices Am. Math. Soc. 45 11 (2001) 1304
    • (2001) Notices Am. Math. Soc. , vol.45 , Issue.11 , pp. 1304
    • Neuhauser, C.1
  • 5
    • 84972503934 scopus 로고
    • Limits of spatial branching processes
    • Wakolbinger A. Limits of spatial branching processes. Bernoulli 1 1/2 (1995) 171
    • (1995) Bernoulli , vol.1 , Issue.1-2 , pp. 171
    • Wakolbinger, A.1
  • 10
    • 0001047828 scopus 로고
    • Long term behaviour of a class of biological models
    • Weinberger H.F. Long term behaviour of a class of biological models. SIAM J. Math. Anal. 13 (1982) 353
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 353
    • Weinberger, H.F.1
  • 11
  • 12
    • 0000791029 scopus 로고
    • Limit theorems for the spread of epidemics and forest fires
    • Cox J.T., and Durrett R. Limit theorems for the spread of epidemics and forest fires. Stochastic Processes Appl. 30 (1988) 171
    • (1988) Stochastic Processes Appl. , vol.30 , pp. 171
    • Cox, J.T.1    Durrett, R.2
  • 13
    • 0001934098 scopus 로고
    • A shape theorem for epidemics and forest fires with finite range interactions
    • Zhang Y. A shape theorem for epidemics and forest fires with finite range interactions. Ann. Probab. 21 4 (1993) 1755
    • (1993) Ann. Probab. , vol.21 , Issue.4 , pp. 1755
    • Zhang, Y.1
  • 14
    • 0033314540 scopus 로고    scopus 로고
    • Stochastic spatial models
    • Durrett R. Stochastic spatial models. SIAM Rev. 41 4 (1999) 677
    • (1999) SIAM Rev. , vol.41 , Issue.4 , pp. 677
    • Durrett, R.1
  • 15
    • 0003175686 scopus 로고
    • Convergence of the solutions of the Kolmogorov equation to travelling waves
    • American Mathematical Society, Providence, Rhode Island
    • Bramsom M. Convergence of the solutions of the Kolmogorov equation to travelling waves. Mem. Amer. Math. Soc. 44 285 (1983) American Mathematical Society, Providence, Rhode Island
    • (1983) Mem. Amer. Math. Soc. , vol.44 , Issue.285
    • Bramsom, M.1
  • 16
    • 0000644794 scopus 로고
    • Spatial contact models for ecological and epidemic spread
    • Mollison D. Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. B. 39 (1977) 283
    • (1977) J. R. Statist. Soc. B. , vol.39 , pp. 283
    • Mollison, D.1
  • 17
    • 33845190454 scopus 로고    scopus 로고
    • J. Radcliffe, L. Rass, Spatial branching and epidemic processes, Mathematical Population Dynamics: Analysis of Heterogeneity, vol. 1, Theory of Epidemics, Wuertz, Winnipeg, 1995, p. 147.
  • 18
    • 4644223220 scopus 로고
    • Deterministic growth-dispersal models and branching random walk
    • Dekking F.M. Deterministic growth-dispersal models and branching random walk. J. Math. Anal. Appl. 192 (1995) 529
    • (1995) J. Math. Anal. Appl. , vol.192 , pp. 529
    • Dekking, F.M.1
  • 19
    • 84980187449 scopus 로고
    • Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piscunov
    • McKean H.P. Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piscunov. Commun. Pure Appl. Math. 28 (1975) 323
    • (1975) Commun. Pure Appl. Math. , vol.28 , pp. 323
    • McKean, H.P.1
  • 20
    • 0011415415 scopus 로고
    • The asymptotic shape of the branching random walk
    • Biggins J.D. The asymptotic shape of the branching random walk. Adv. Appl. Prob. 10 (1978) 62
    • (1978) Adv. Appl. Prob. , vol.10 , pp. 62
    • Biggins, J.D.1
  • 22
    • 21344435220 scopus 로고
    • The growth and spread of the general branching random walk
    • Biggins J.D. The growth and spread of the general branching random walk. Ann. Appl. Prob. 5 (1995) 1008
    • (1995) Ann. Appl. Prob. , vol.5 , pp. 1008
    • Biggins, J.D.1
  • 23
    • 0001944424 scopus 로고
    • Run for your life: a note on the asymptotic speed of propagation of an epidemic
    • Diekmann O. Run for your life: a note on the asymptotic speed of propagation of an epidemic. J. differen. Equat. 33 (1979) 58
    • (1979) J. differen. Equat. , vol.33 , pp. 58
    • Diekmann, O.1
  • 24
    • 0022592111 scopus 로고
    • The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic
    • Radcliffe J., and Rass L. The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic. J. Math. Biol. 23 (1986) 341
    • (1986) J. Math. Biol. , vol.23 , pp. 341
    • Radcliffe, J.1    Rass, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.