메뉴 건너뛰기




Volumn 9, Issue 3, 2012, Pages 461-485

Stochastic models for competing species with a shared pathogen

Author keywords

Branching processes; Competition; Continuous time Markov chains; SIS model; Stochastic differential equations

Indexed keywords

ARTICLE; BACTERIUM; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; COMPUTER SIMULATION; EPIDEMIC; FUNGUS; HOST PATHOGEN INTERACTION; HUMAN; PATHOGENICITY; POPULATION DYNAMICS; PROBABILITY; STATISTICS; VIRUS;

EID: 84864845417     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2012.9.461     Document Type: Article
Times cited : (12)

References (56)
  • 1
    • 34547655997 scopus 로고    scopus 로고
    • Modeling with itô stochastic difierential equations
    • Springer, Dordrecht, The Netherlands
    • E. Allen, "Modeling With Itô Stochastic Difierential Equations," Mathematical Modelling: Theory and Applications, 22, Springer, Dordrecht, The Netherlands, 2007.
    • (2007) Mathematical Modelling: Theory and Applications , vol.22
    • Allen, E.1
  • 2
    • 40549105092 scopus 로고    scopus 로고
    • Construction of equivalent stochastic difierential equation models
    • E. J. Allen, L. J. S. Allen, A. Arciniega and P. Greenwood, Construction of equivalent stochastic difierential equation models, Stoch. Anal. Appl., 26 (2008), 274-297.
    • (2008) Stoch. Anal. Appl. , vol.26 , pp. 274-297
    • Allen, E.J.1    Allen, L.J.S.2    Arciniega, A.3    Greenwood, P.4
  • 5
    • 85015746533 scopus 로고    scopus 로고
    • Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens
    • L. J. S. Allen and N. Kirupaharan, Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens, Int. J. Numer. Anal. Modeling, 2 (2005), 329-344.
    • (2005) Int. J. Numer. Anal. Modeling , vol.2 , pp. 329-344
    • Allen, L.J.S.1    Kirupaharan, N.2
  • 6
    • 0023527189 scopus 로고
    • The invasion, persistence and spread of infectious diseases with animal and plant communities
    • R. M. Anderson and R. M. May, The invasion, persistence and spread of infectious diseases with animal and plant communities, Phil. Trans. R. Soc. Lond. B, 314 (1986), 533-570.
    • (1986) Phil. Trans. R. Soc. Lond. B , vol.314 , pp. 533-570
    • Anderson, R.M.1    May, R.M.2
  • 7
    • 0003812093 scopus 로고
    • The elements of stochastic processes with applications to the natural sciences
    • Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York
    • N. T. J. Bailey, "The Elements of Stochastic Processes with Applications to the Natural Sciences," Reprint of the 1964 original, Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1990.
    • (1990) Reprint of the 1964 original
    • Bailey, N.T.J.1
  • 8
    • 0011485892 scopus 로고
    • The relevance of stochastic models for large-scale epidemiological phenomena
    • M. S. Bartlett, The relevance of stochastic models for large-scale epidemiological phenomena, Appl. Statist., 13 (1965), 2-8.
    • (1965) Appl. Statist. , vol.13 , pp. 2-8
    • Bartlett, M.S.1
  • 9
    • 0026499443 scopus 로고
    • Disease and community structure: The importance of host self-regulation in a host-host-pathogen model
    • M. Begon, R. G. Bowers, N. Kadianakis and D. E. Hodgkinson, Disease and community structure: The importance of host self-regulation in a host-host-pathogen model, Am. Nat., 139 (1992), 1131-1150.
    • (1992) Am. Nat. , vol.139 , pp. 1131-1150
    • Begon, M.1    Bowers, R.G.2    Kadianakis, N.3    Hodgkinson, D.E.4
  • 12
    • 0031558229 scopus 로고    scopus 로고
    • Community structure and the interplay between interspecific infection and competition
    • DOI 10.1006/jtbi.1997.0418
    • R. G. Bowers and J. Turner, Community structure and the interplay between interspecific infection and competition, J. Theor. Biol., 187 (1997), 95-109. (Pubitemid 27338670)
    • (1997) Journal of Theoretical Biology , vol.187 , Issue.1 , pp. 95-109
    • Bowers, R.G.1    Turner, J.2
  • 14
    • 8744230965 scopus 로고    scopus 로고
    • Population dynamics of pathogens with multiple host species
    • DOI 10.1086/424681
    • A. Dobson, Population dynamics of pathogens with multiple host species, Am. Nat., 164 (2004), S64-S78. (Pubitemid 39509006)
    • (2004) American Naturalist , vol.164 , Issue.5
    • Dobson, A.1
  • 15
    • 85085398796 scopus 로고    scopus 로고
    • Mutual invadability implies coexistence in spatial models
    • R. Durrett, Mutual invadability implies coexistence in spatial models, Mem. Am. Math. Soc., 156 (2002), viii+118 pp.
    • (2002) Mem. Am. Math. Soc. , vol.156 , pp. 126
    • Durrett, R.1
  • 16
    • 66149114872 scopus 로고    scopus 로고
    • Special invited paper: Coexistence in stochastic spatial models
    • R. Durrett, Special invited paper: Coexistence in stochastic spatial models, Ann. Appl. Probab., 19 (2009), 477-496.
    • (2009) Ann. Appl. Probab. , vol.19 , pp. 477-496
    • Durrett, R.1
  • 17
    • 0031285155 scopus 로고    scopus 로고
    • Coexistence results for some competition models
    • R. Durrett and C. Neuhauser, Coexistence results for some competition models, Ann. Appl. Probab., 7 (1997), 10-45.
    • (1997) Ann. Appl. Probab. , vol.7 , pp. 10-45
    • Durrett, R.1    Neuhauser, C.2
  • 18
    • 0035214189 scopus 로고    scopus 로고
    • Disease persistence and apparent competition in a three-host community: An empirical and analytical study of large-scale, wild populations
    • DOI 10.1046/j.0021-8790.2001.00558.x
    • L. Gilbert, R. Norman, K. M. Laurenson, H. W. Reid and P. J. Hudson, Disease persistence and apparent competition in a three-host community: An empirical and analytical study of large-scale, wild populations, J. Anim. Ecol., 70 (2001), 1053-1061. (Pubitemid 33146354)
    • (2001) Journal of Animal Ecology , vol.70 , Issue.6 , pp. 1053-1061
    • Gilbert, L.1    Norman, R.2    Laurenson, K.M.3    Reid, H.W.4    Hudson, P.J.5
  • 20
    • 0031557668 scopus 로고    scopus 로고
    • Infected coexistence instability with and without density-dependent regulation
    • DOI 10.1006/jtbi.1996.0309
    • J. V. Greenman and P. J. Hudson, Infected coexistence instability with and without density-dependent regulation, J. Theor. Biol., 185 (1997), 345-356. (Pubitemid 27192504)
    • (1997) Journal of Theoretical Biology , vol.185 , Issue.3 , pp. 345-356
    • Greenman, J.V.1    Hudson, P.J.2
  • 21
    • 79954677689 scopus 로고    scopus 로고
    • The probability of extinction in a bovine respiratory syncytial virus epidemic model
    • M. Grifiths and D. Greenhalgh, The probability of extinction in a bovine respiratory syncytial virus epidemic model, Math. Biosci., 231 (2011), 144-158.
    • (2011) Math. Biosci. , vol.231 , pp. 144-158
    • Grifiths, M.1    Greenhalgh, D.2
  • 23
    • 0037418117 scopus 로고    scopus 로고
    • An SIRS epidemic model of two competitive species
    • PII S0895717702003266
    • L. Han, Z. Ma and T. Shi, An SIRS epidemic model of two competitive species, Math. Comput. Model., 37 (2003), 87-108. (Pubitemid 36229757)
    • (2003) Mathematical and Computer Modelling , vol.37 , Issue.1-2 , pp. 87-108
    • Han, L.1    Ma, Z.2    Shi, T.3
  • 25
    • 0003370813 scopus 로고
    • The theory of branching processes
    • Bd. 119, Springer-Verlag, Berlin, Prentice-Hall, Inc., Englewood Clifis, NJ
    • T. E. Harris, "The Theory of Branching Processes," Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, Prentice-Hall, Inc., Englewood Clifis, NJ, 1963.
    • (1963) Die Grundlehren der Mathematischen Wissenschaften
    • Harris, T.E.1
  • 26
    • 33750029631 scopus 로고    scopus 로고
    • How parasites affect interactions between competitors and predators
    • DOI 10.1111/j.1461-0248.2006.00964.x
    • M. J. Hatcher, J. T. A. Dick and A. M. Dunn, How parasites afiect interactions between competitors and predators, Ecol. Lett., 9 (2006), 1253-1271. (Pubitemid 44571667)
    • (2006) Ecology Letters , vol.9 , Issue.11 , pp. 1253-1271
    • Hatcher, M.J.1    Dick, J.T.A.2    Dunn, A.M.3
  • 27
    • 44949114109 scopus 로고    scopus 로고
    • Modeling and simulating chemical reactions
    • DOI 10.1137/060666457
    • D. J. Higham, Modeling and simulating chemical reactions, SIAM Rev., 50 (2008), 347-368. (Pubitemid 351803949)
    • (2008) SIAM Review , vol.50 , Issue.2 , pp. 347-368
    • Higham, D.J.1
  • 28
    • 33750013749 scopus 로고    scopus 로고
    • Chapter 2: Extending the principles of community ecology to address the epidemiology of host-pathogen systems
    • (eds. S. K. Collinge and C. Ray), Oxford Univ. Press, Oxford
    • R. D. Holt and A. P. Dobson, Chapter 2: Extending the principles of community ecology to address the epidemiology of host-pathogen systems, in "Disease Ecology: Community Structure and Pathogen Dynamics" (eds. S. K. Collinge and C. Ray), Oxford Univ. Press, Oxford, (2006), 2-27.
    • (2006) Disease Ecology: Community Structure and Pathogen Dynamics , pp. 2-27
    • Holt, R.D.1    Dobson, A.P.2
  • 29
    • 0022191646 scopus 로고
    • Infectious disease and species coexistence: A model of Lotka- Volterra form
    • DOI 10.1086/284409
    • R. D. Holt and J. Pickering, Infectious disease and species coexistence: A model of Lotka-Volterra form, Am. Nat., 126 (1985), 196-211. (Pubitemid 17245191)
    • (1985) American Naturalist , vol.126 , Issue.2 , pp. 196-211
    • Holt, R.D.1    Pickering, J.2
  • 30
    • 0031691011 scopus 로고    scopus 로고
    • Competition mediated by parasites: Biological and theoretical progress
    • DOI 10.1016/S0169-5347(98)01475-X, PII S016953479801475X
    • P. Hudson and J. Greenman, Competition mediated by parasites: Biological and theoretical progress, Trends Ecol. Evol., 13 (1998), 387-390. (Pubitemid 28430677)
    • (1998) Trends in Ecology and Evolution , vol.13 , Issue.10 , pp. 387-390
    • Hudson, P.1    Greenman, J.2
  • 31
    • 0003882770 scopus 로고
    • Wiley Series in Probability and Mathematical StatisticsApplied Probability and Statistics, Wiley-Interscience [John Wiley & Sons], London-New York-Sydney
    • P. Jagers, "Branching Processes with Biological Applications," Wiley Series in Probability and Mathematical StatisticsApplied Probability and Statistics, Wiley-Interscience [John Wiley & Sons], London-New York-Sydney, 1975.
    • (1975) Branching Processes with Biological Applications
    • Jagers, P.1
  • 32
    • 0003730487 scopus 로고
    • 2nd edition, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London
    • S. T. Karlin and H. M. Taylor, "A First Course in Stochastic Processes," 2nd edition, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975.
    • (1975) A First Course in Stochastic Processes
    • Karlin, S.T.1    Taylor, H.M.2
  • 33
    • 0032874846 scopus 로고    scopus 로고
    • Pathogen reverses competition between larval amphibians
    • J. M. Kiesecker and A. R. Blaustein, Pathogen reverses competition between larval amphibians, Ecology, 80 (1999), 2442-2448. (Pubitemid 29485614)
    • (1999) Ecology , vol.80 , Issue.7 , pp. 2442-2448
    • Kiesecker, J.M.1    Blaustein, A.R.2
  • 34
    • 0003568337 scopus 로고
    • Numerical solution of stochastic difierential equations
    • Springer-Verlag, Berlin
    • P. Kloeden and E. Platen, "Numerical Solution of Stochastic Difierential Equations," Applications of Mathematics (New York), 23, Springer-Verlag, Berlin, 1992.
    • (1992) Applications of Mathematics (New York) , vol.23
    • Kloeden, P.1    Platen, E.2
  • 35
    • 33750495782 scopus 로고    scopus 로고
    • A spatially explicit model for competition among specialists and generalists in a heterogeneous environment
    • DOI 10.1214/105051606000000394
    • N. Lanchier and C. Neuhauser, A spatially explicit model for competition among specialists and generalists in a heterogeneous environment , Ann. Appl. Probab., 16 (2006), 1385-1410. (Pubitemid 44662196)
    • (2006) Annals of Applied Probability , vol.16 , Issue.3 , pp. 1385-1410
    • Lanchier, N.1    Neuhauser, C.2
  • 36
    • 33645693869 scopus 로고    scopus 로고
    • Stochastic spatial models of host-pathogen and host-mutualist interactions
    • DOI 10.1214/105051605000000782
    • N. Lanchier and C. Neuhauser, Stochastic spatial models of host-pathogen and host-mutualist interactions. I , Ann. Appl. Probab., 16 (2006), 448-474. (Pubitemid 43535940)
    • (2006) Annals of Applied Probability , vol.16 , Issue.1 , pp. 448-474
    • Lanchier, N.1    Neuhauser, C.2
  • 38
    • 0000268789 scopus 로고
    • Nonlinear aspects of competition between three species Special issue on mathematics and the social and biological sciences
    • R. M. May and W. J. Leonard, Nonlinear aspects of competition between three species, Special issue on mathematics and the social and biological sciences, SIAM J. Appl. Math., 29 (1975), 243-253.
    • (1975) SIAM J. Appl. Math. , vol.29 , pp. 243-253
    • May, R.M.1    Leonard, W.J.2
  • 39
    • 0035358852 scopus 로고    scopus 로고
    • How should pathogen transmission be modelled?
    • DOI 10.1016/S0169-5347(01)02144-9, PII S0169534701021449
    • H. McCallum, N. Barlow and J. Hone, How should pathogen transmission be modelled?, Trends Ecol. Evol., 16 (2001), 295-300. (Pubitemid 32706645)
    • (2001) Trends in Ecology and Evolution , vol.16 , Issue.6 , pp. 295-300
    • McCallum, H.1    Barlow, N.2    Hone, J.3
  • 41
    • 77951289404 scopus 로고    scopus 로고
    • Stochastic SIS and SIR multihost epidemic models
    • Hindawi Publ. Corp., New York
    • R. K. McCormack and L. J. S. Allen, Stochastic SIS and SIR multihost epidemic models, in "Difierential & Difierence Eqns. Appl.," Hindawi Publ. Corp., New York, (2006), 775-785.
    • (2006) Difierential & Difierence Eqns. Appl. , pp. 775-785
    • McCormack, R.K.1    Allen, L.J.S.2
  • 42
    • 33847679359 scopus 로고    scopus 로고
    • Disease emergence in multi-host epidemic models
    • DOI 10.1093/imammb/dql021
    • R. K. McCormack and L. J. S. Allen, Disease emergence in multi-host epidemic models, Math. Med. Biol., 24 (2007), 17-34. (Pubitemid 46358981)
    • (2007) Mathematical Medicine and Biology , vol.24 , Issue.1 , pp. 17-34
    • McCormack, R.K.1    Allen, L.J.S.2
  • 43
    • 0038895338 scopus 로고
    • Multitype branching processes. Theory and applications
    • American Elsevier Publishing Co., Inc., New York
    • C. J. Mode, "Multitype Branching Processes. Theory and Applications," Modern Analytic and Computational Methods in Science and Mathematics, No. 34 , American Elsevier Publishing Co., Inc., New York, 1971.
    • (1971) Modern Analytic and Computational Methods in Science and Mathematics , Issue.34
    • Mode, C.J.1
  • 44
    • 85027940406 scopus 로고    scopus 로고
    • Spatiotemporal model of barley and cereal yellow dwarf virus transmission dynamics with seasonality and plant competition
    • S. M. Moore, C. A. Manore, V. A. Bokil, E. T. Borer and P. R. Hosseini, Spatiotemporal model of barley and cereal yellow dwarf virus transmission dynamics with seasonality and plant competition, Bull. Math. Biol., 73 (2011), 2707-2730.
    • (2011) Bull. Math. Biol. , vol.73 , pp. 2707-2730
    • Moore, S.M.1    Manore, C.A.2    Bokil, V.A.3    Borer, E.T.4    Hosseini, P.R.5
  • 45
    • 0033274921 scopus 로고    scopus 로고
    • An explicitly spatial version of the Lotka-Volterra model with interspecific competition
    • C. Neuhauser and S. W. Pacala, An explicitly spatial version of the Lotka-Volterra model with interspecific competition, Ann. Appl. Probab., 9 (1999), 1226-1259.
    • (1999) Ann. Appl. Probab. , vol.9 , pp. 1226-1259
    • Neuhauser, C.1    Pacala, S.W.2
  • 46
    • 0033533378 scopus 로고    scopus 로고
    • Persistence of tick-borne virus in the presence of multiple host species: Tick reservoirs and parasite mediated competition
    • DOI 10.1006/jtbi.1999.0982
    • R. Norman, R. G. Bowers, M. Begon and P. J. Hudson, Persistence of tick-borne virus in the presence of multiple host species: Tick reservoirs and parasite mediated competition, J. Theor. Biol., 200 (1999), 111-118. (Pubitemid 29481595)
    • (1999) Journal of Theoretical Biology , vol.200 , Issue.1 , pp. 111-118
    • Norman, R.1    Bowers, R.G.2    Begon, M.3    Hudson, P.J.4
  • 47
    • 0003578016 scopus 로고
    • The University Series in Mathematics, Plenum Press, New York
    • J. M. Ortega, "Matrix Theory. A Second Course," The University Series in Mathematics, Plenum Press, New York, 1987.
    • (1987) Matrix Theory. A Second Course
    • Ortega, J.M.1
  • 50
    • 0033969580 scopus 로고    scopus 로고
    • Field evidence for apparent competition mediated via the shared parasites of two gamebird species
    • D. M. Tompkins, R. A. H. Draycott and P. J. Hudson, Field evidence for apparent competition mediated via the shared parasites of two gamebird species, Ecol. Lett., 3 (2000), 10-14. (Pubitemid 30063426)
    • (2000) Ecology Letters , vol.3 , Issue.1 , pp. 10-14
    • Tompkins, D.M.1    Draycott, R.A.H.2    Hudson, P.J.3
  • 51
    • 0242584396 scopus 로고    scopus 로고
    • Ecological replacement of native red squirrels by invasive greys driven by disease
    • DOI 10.1046/j.1461-0248.2003.00417.x
    • D. M. Tompkins, A. R. White and M. Boots, Ecological replacement of native red squirrels by invasive greys driven by disease, Ecol. Lett., 6 (2003), 189-196. (Pubitemid 36453453)
    • (2003) Ecology Letters , vol.6 , Issue.3 , pp. 189-196
    • Tompkins, D.M.1    White, A.R.2    Boots, M.3
  • 52
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • DOI 10.1016/S0025-5564(02)00108-6, PII S0025556402001086
    • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. (Pubitemid 35304346)
    • (2002) Mathematical Biosciences , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2
  • 53
  • 54
    • 0035669003 scopus 로고    scopus 로고
    • The efiects of diseases on competing species
    • E. Venturino, The efiects of diseases on competing species, Math. Biosci., 174 (2001), 111-131.
    • (2001) Math. Biosci. , vol.174 , pp. 111-131
    • Venturino, E.1
  • 55
    • 0001236565 scopus 로고
    • The outcome of a stochastic epidemic: A note on Bailey's paper
    • P. Whittle, The outcome of a stochastic epidemic: A note on Bailey's paper, Biometrika, 42 (1955), 116-122.
    • (1955) Biometrika , vol.42 , pp. 116-122
    • Whittle, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.