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Volumn 195, Issue 2, 2003, Pages 430-470

Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models

Author keywords

Asymptotic speeds of spread; Minimal wave speeds; Nonlinear integral equations; Population models; Traveling waves

Indexed keywords


EID: 0345116416     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00175-X     Document Type: Article
Times cited : (327)

References (43)
  • 1
    • 0344578958 scopus 로고    scopus 로고
    • Monotone travelling fronts in an age-structured reaction-diffusion model of a single species
    • J. Al-Omari, S.A. Gourley, Monotone travelling fronts in an age-structured reaction-diffusion model of a single species, J. Math. Biol. 45 (2002) 294-312.
    • (2002) J. Math. Biol. , vol.45 , pp. 294-312
    • Al-Omari, J.1    Gourley, S.A.2
  • 2
    • 0002899831 scopus 로고
    • The asymptotic speed of propagation of a simple epidemic
    • W.E. Fitzgibbon, H.F. Walker (Eds.), Pitman, London
    • D.G. Aronson, The asymptotic speed of propagation of a simple epidemic, in: W.E. Fitzgibbon, H.F. Walker (Eds.), Nonlinear Diffusion, Pitman, London, 077, pp. 1-23.
    • (1977) Nonlinear Diffusion , pp. 1-23
    • Aronson, D.G.1
  • 3
    • 0002488752 scopus 로고
    • Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation
    • Lecture Notes in Mathematics, J.A. Goldstein (Ed.), Springer, Berlin
    • D.G. Aronson, H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in: J.A. Goldstein (Ed.), Partial Differential Equations and Related Topics, Lecture Notes in Mathematics, Vol. 446, Springer, Berlin, 1975, pp. 5-49.
    • (1975) Partial Differential Equations and Related Topics , vol.446 , pp. 5-49
    • Aronson, D.G.1    Weinberger, H.F.2
  • 4
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusion arising in population dynamics
    • D.G. Aronson, H.F. Weinberger, Multidimensional nonlinear diffusion arising in population dynamics, Adv. in Math. 30 (1978) 33-76.
    • (1978) Adv. in Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 6
    • 84971127850 scopus 로고
    • Deterministic epidemic waves of critical velocity
    • K.J. Brown, J. Carr, Deterministic epidemic waves of critical velocity, Math. Proc. Cambridge Philos. Soc. 81 (1977) 431-433.
    • (1977) Math. Proc. Cambridge Philos. Soc. , vol.81 , pp. 431-433
    • Brown, K.J.1    Carr, J.2
  • 7
    • 0019807845 scopus 로고
    • Convergence to equilibrium states for a reaction-diffusion system modeling the spatial spread of a class of bacterial and viral diseases
    • V. Capasso, L. Maddalena, Convergence to equilibrium states for a reaction-diffusion system modeling the spatial spread of a class of bacterial and viral diseases, J. Math. Biol. 13 (1981) 173-184.
    • (1981) J. Math. Biol. , vol.13 , pp. 173-184
    • Capasso, V.1    Maddalena, L.2
  • 8
    • 0345009973 scopus 로고
    • Saddle point behavior for a reaction-diffusion system: Application to a class of epidemic models
    • V. Capasso, L. Maddalena, Saddle point behavior for a reaction-diffusion system: application to a class of epidemic models, Math. Comput. Simulation 24 (1982) 540-547.
    • (1982) Math. Comput. Simulation , vol.24 , pp. 540-547
    • Capasso, V.1    Maddalena, L.2
  • 9
    • 85030922574 scopus 로고
    • A threshold theorem for a reaction-diffusion epidemic system
    • A.R. Aftabizadeh (Ed.), Ohio University Press, Athens, OH
    • V. Capasso, H.R. Thieme, A threshold theorem for a reaction-diffusion epidemic system, in: A.R. Aftabizadeh (Ed.), Differential Equations and Applications, Ohio University Press, Athens, OH, 1989, pp. 128-131
    • (1989) Differential Equations and Applications , pp. 128-131
    • Capasso, V.1    Thieme, H.R.2
  • 10
    • 0031117716 scopus 로고    scopus 로고
    • Analysis of a reaction-diffusion modeling man-environment-man epidemics
    • V. Capasso, R.E. Wilson, Analysis of a reaction-diffusion modeling man-environment-man epidemics, SIAM J. Appl. Math. 57 (1997) 327-346.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 327-346
    • Capasso, V.1    Wilson, R.E.2
  • 11
    • 0018184969 scopus 로고
    • Thresholds and traveling waves for the geographical spread of infection
    • O. Diekmann, Thresholds and traveling waves for the geographical spread of infection, J. Math. Biol. 6 (1978) 109-130.
    • (1978) J. Math. Biol. , vol.6 , pp. 109-130
    • Diekmann, O.1
  • 12
    • 0001944424 scopus 로고
    • Run for your life, a note on the asymptotic speed of propagation of an epidemic
    • O. Diekmann, Run for your life, a note on the asymptotic speed of propagation of an epidemic, J. Differential Equations 33 (1979) 58-73.
    • (1979) J. Differential Equations , vol.33 , pp. 58-73
    • Diekmann, O.1
  • 13
    • 0000360728 scopus 로고
    • On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal.: Theory
    • O. Diekmann, H.G. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal.: Theory, Methods Appl. 2 (1978) 721-737.
    • (1978) Methods Appl. , vol.2 , pp. 721-737
    • Diekmann, O.1    Kaper, H.G.2
  • 15
    • 33746918065 scopus 로고    scopus 로고
    • Wavefronts and global stability in a time-delayed population model with stage structure
    • preprint
    • S.A. Gourley, Y. Kuang, Wavefronts and global stability in a time-delayed population model with stage structure, preprint, 2002.
    • (2002)
    • Gourley, S.A.1    Kuang, Y.2
  • 16
    • 0036729759 scopus 로고    scopus 로고
    • Spreading speed and linear determinacy for two-species competition models
    • M.A. Lewis, B. Li, H.F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol. 45 (2002) 219-233.
    • (2002) J. Math. Biol. , vol.45 , pp. 219-233
    • Lewis, M.A.1    Li, B.2    Weinberger, H.F.3
  • 17
    • 0024639645 scopus 로고
    • Biological growth and spread modeled by systems of recursions. I. Mathematical theory
    • R. Lui, Biological growth and spread modeled by systems of recursions. I. Mathematical theory, Math. Biosci. 93 (1989) 269-295.
    • (1989) Math. Biosci. , vol.93 , pp. 269-295
    • Lui, R.1
  • 18
    • 0024639610 scopus 로고
    • Biological growth and spread modeled by systems of recursions. II. Biological theory
    • R. Lui, Biological growth and spread modeled by systems of recursions. II. Biological theory, Math. Biosci. 93 (1989) 297-312.
    • (1989) Math. Biosci. , vol.93 , pp. 297-312
    • Lui, R.1
  • 19
    • 0035836903 scopus 로고    scopus 로고
    • Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem
    • S. Ma, Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem, J. Differential Equations 171 (2001) 294-314.
    • (2001) J. Differential Equations , vol.171 , pp. 294-314
    • Ma, S.1
  • 20
    • 84966246501 scopus 로고
    • Abstract functional differential equations and reaction-diffusion systems
    • R.H. Martin, H.L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Amer. Math. Soc. 321 (1990) 1-44.
    • (1990) Trans. Amer. Math. Soc. , vol.321 , pp. 1-44
    • Martin, R.H.1    Smith, H.L.2
  • 22
    • 0020515976 scopus 로고
    • Wave solutions for the deterministic non-reducible n-type epidemic
    • J. Radcliffe, L. Rass, Wave solutions for the deterministic non-reducible n-type epidemic, J. Math. Biol. 17 (1983) 45-66.
    • (1983) J. Math. Biol. , vol.17 , pp. 45-66
    • Radcliffe, J.1    Rass, L.2
  • 23
    • 0021251991 scopus 로고
    • The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic
    • J. Radcliffe, L. Rass, The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic, J. Math. Biol. 19 (1984) 303-308.
    • (1984) J. Math. Biol. , vol.19 , pp. 303-308
    • Radcliffe, J.1    Rass, L.2
  • 24
    • 0022592111 scopus 로고
    • The asymptotic spread of propagation of the deterministic non-reducible n-type epidemic
    • J. Radcliffe, L. Rass, The asymptotic spread of propagation of the deterministic non-reducible n-type epidemic, J. Math. Biol. 23 (1986) 341-359.
    • (1986) J. Math. Biol. , vol.23 , pp. 341-359
    • Radcliffe, J.1    Rass, L.2
  • 25
    • 0001584326 scopus 로고
    • Asymptotic behavior and traveling wave solutions for parabolic functional differential equations
    • K.W. Schaaf, Asymptotic behavior and traveling wave solutions for parabolic functional differential equations, Trans. Amer. Math. Soc. 302 (1987) 587-615.
    • (1987) Trans. Amer. Math. Soc. , vol.302 , pp. 587-615
    • Schaaf, K.W.1
  • 26
    • 0012666175 scopus 로고
    • Travelling front solutions for integrodifferential equations II
    • Lecture Notes in Biomathematics, W. Jäger, H. Rost, P. Tautu (Eds.), Springer
    • Schumacher, Travelling front solutions for integrodifferential equations II, in: W. Jäger, H. Rost, P. Tautu (Eds.), Biological Growth and Spread, Lecture Notes in Biomathematics, Vol. 38, Springer, 1980, pp. 296-309.
    • (1980) Biological Growth and Spread , vol.38 , pp. 296-309
    • Schumacher, A.1
  • 27
    • 0001676484 scopus 로고
    • Strongly order preserving semiflows generated by functional differential equations
    • H.L. Smith, H.R. Thieme, Strongly order preserving semiflows generated by functional differential equations, J. Differential Equations 93 (1991) 332-363.
    • (1991) J. Differential Equations , vol.93 , pp. 332-363
    • Smith, H.L.1    Thieme, H.R.2
  • 28
    • 0040807398 scopus 로고    scopus 로고
    • Global asymptotic stability of traveling waves in delayed reaction-diffusion equations
    • H.L. Smith, X.-Q. Zhao, Global asymptotic stability of traveling waves in delayed reaction-diffusion equations, SIAM J. Math. Anal. 31 (2000) 514-534.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 514-534
    • Smith, H.L.1    Zhao, X.-Q.2
  • 29
    • 32044440101 scopus 로고    scopus 로고
    • A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains
    • J.W.-H. So, J. Wu, X. Zou, A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains, Proc. Roy. Soc. London Ser. A 457 (2001) 1841-1853.
    • (2001) Proc. Roy. Soc. London Ser. A , vol.457 , pp. 1841-1853
    • So, J.W.-H.1    Wu, J.2    Zou, X.3
  • 30
    • 0008260279 scopus 로고
    • Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations
    • H.R. Thieme, Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math. 306 (1979) 94-121.
    • (1979) J. Reine Angew. Math. , vol.306 , pp. 94-121
    • Thieme, H.R.1
  • 31
    • 0018570848 scopus 로고
    • Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread
    • H.R. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol. 8 (1979) 173-187.
    • (1979) J. Math. Biol. , vol.8 , pp. 173-187
    • Thieme, H.R.1
  • 32
    • 0345009977 scopus 로고
    • On a class of Hammerstein integral equations
    • H.R. Thieme, On a class of Hammerstein integral equations, Manuscripta Math. 29 (1979) 49-84.
    • (1979) Manuscripta Math. , vol.29 , pp. 49-84
    • Thieme, H.R.1
  • 34
  • 36
    • 85030924975 scopus 로고
    • V.A. Volpert, Translation of Mathematical Monographs, American Mathematical Society, Providence, RI
    • A.I. Volpert, V.A. Volpert, V.A. Volpert, Traveling Wave Solutions of Parabolic Systems, Translation of Mathematical Monographs, Vol. 140, American Mathematical Society, Providence, RI. 1994.
    • (1994) Traveling Wave Solutions of Parabolic Systems , vol.140
    • Volpert, A.I.1    Volpert, V.A.2
  • 37
    • 0345009974 scopus 로고
    • Some deterministic models for the spread of genetic and other alterations
    • Lecture Notes in Biomathematics, W. Jäger, H. Rost, P. Tautu (Eds.), Springer, Berlin
    • H.F. Weinberger, Some deterministic models for the spread of genetic and other alterations, in: W. Jäger, H. Rost, P. Tautu (Eds.), Biological Growth and Spread, Lecture Notes in Biomathematics, Vol. 38, Springer, Berlin, 1981, pp. 320-333.
    • (1981) Biological Growth and Spread , vol.38 , pp. 320-333
    • Weinberger, H.F.1
  • 38
    • 0001047828 scopus 로고
    • Long time behavior of a class of biological models
    • H.F. Weinberger, Long time behavior of a class of biological models, SIAM J. Math. Anal. 13 (1982) 353-396.
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 353-396
    • Weinberger, H.F.1
  • 39
    • 0036725475 scopus 로고    scopus 로고
    • Analysis of linear determinacy for spread in cooperative models
    • H.F. Weinberger, M.A. Lewis, B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol. 45 (2002) 183-218.
    • (2002) J. Math. Biol. , vol.45 , pp. 183-218
    • Weinberger, H.F.1    Lewis, M.A.2    Li, B.3
  • 41
    • 0037059086 scopus 로고    scopus 로고
    • Diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations
    • J. Wu, X.-Q. Zhao, Diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations, J. Differential Equations 186 (2002) 470-484.
    • (2002) J. Differential Equations , vol.186 , pp. 470-484
    • Wu, J.1    Zhao, X.-Q.2
  • 42
    • 0343717093 scopus 로고    scopus 로고
    • Traveling wave fronts of reaction-diffusion systems with delay
    • J. Wu, X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dyn. Differential Equations 13 (2001) 651-687.
    • (2001) J. Dyn. Differential Equations , vol.13 , pp. 651-687
    • Wu, J.1    Zou, X.2


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