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Volumn 412, Issue , 2014, Pages 137-148

Effect of time delay on pattern dynamics in a spatial epidemic model

Author keywords

Epidemic model; Nonlinear incidence rate; Patterns; Time delay; Turing instability

Indexed keywords

BIOLOGICAL SYSTEMS; HOPF BIFURCATION; TIME DELAY; TIMING CIRCUITS;

EID: 84904327259     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2014.06.038     Document Type: Article
Times cited : (29)

References (63)
  • 3
    • 84880312977 scopus 로고    scopus 로고
    • Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: A population-based study of laboratory-confirmed cases
    • B.J. Cowling, L.M. Jin, and E. Lau et al. Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases The Lancet 382 2013 129 137
    • (2013) The Lancet , vol.382 , pp. 129-137
    • Cowling, B.J.1    Jin, L.M.2    Lau, E.3
  • 4
    • 84893538720 scopus 로고    scopus 로고
    • Epidemiology of human infections with avian influenza A(H7N9) virus in China
    • Q. Li, L. Zhou, M.H. Zhou, Z.P. Chen, and F.R. Li et al. Epidemiology of human infections with avian influenza A(H7N9) virus in China N. Engl. J. Med. 370 2014 520 532
    • (2014) N. Engl. J. Med. , vol.370 , pp. 520-532
    • Li, Q.1    Zhou, L.2    Zhou, M.H.3    Chen, Z.P.4    Li, F.R.5
  • 7
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 42 2000 599 653
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 10
    • 0015711463 scopus 로고
    • Recurrent outbreaks of measles, chickenpox and mumps II
    • J.A. Yorke, and W.P. London Recurrent outbreaks of measles, chickenpox and mumps II Am. J. Epidemiol. 98 1973 469 482
    • (1973) Am. J. Epidemiol. , vol.98 , pp. 469-482
    • Yorke, J.A.1    London, W.P.2
  • 11
    • 0018041874 scopus 로고
    • A generalization of the Kermack-McKendrick deterministic epidemic model
    • DOI 10.1016/0025-5564(78)90006-8
    • V. Capasso, and G. Serio A generalization of the Kermack-McKendrick deterministic epidemic model Math. Biosci. 42 1978 43 61 (Pubitemid 9117153)
    • (1978) Mathematical Biosciences , vol.42 , Issue.1-2 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 12
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • DOI 10.1007/BF00276956
    • W.M. Liu, S.A. Levin, and Y. Iwasa Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models J. Math. Biol. 23 1986 187 204 (Pubitemid 16153721)
    • (1985) Journal of Mathematical Biology , vol.23 , Issue.2 , pp. 187-204
    • Liu, W.-M.1    Levin, S.A.2    Iwasa, Y.3
  • 13
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • W.M. Liu, H.W. Hethcote, and S.A. Levin Dynamical behavior of epidemiological models with nonlinear incidence rates J. Math. Biol. 25 1987 359 380
    • (1987) J. Math. Biol. , vol.25 , pp. 359-380
    • Liu, W.M.1    Hethcote, H.W.2    Levin, S.A.3
  • 14
    • 0036229603 scopus 로고    scopus 로고
    • The interplay between determinism and stochasticity in childhood diseases
    • DOI 10.1086/339467
    • P. Rohani, M.J. Keeling, and B.T. Grenfell The interplay between determinism and stochasticity in childhood diseases Am. Nat. 159 2002 469 481 (Pubitemid 34443778)
    • (2002) American Naturalist , vol.159 , Issue.5 , pp. 469-481
    • Rohani, P.1    Keeling, M.J.2    Grenfell, B.T.3
  • 15
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • DOI 10.1126/science.287.5453.667
    • D.J.D. Earn, P. Rohani, B. Bolker, and B.T. Grenfell A simple model for complex dynamical transitions in epidemics Science 287 2000 667 670 (Pubitemid 30070917)
    • (2000) Science , vol.287 , Issue.5453 , pp. 667-670
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 17
    • 0034923771 scopus 로고    scopus 로고
    • Endemic models with arbitrarily distributed periods of infection i
    • Z. Feng, and H.R. Thieme Endemic models with arbitrarily distributed periods of infection I SIAM J. Appl. Math. 61 2000 803 833
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 803-833
    • Feng, Z.1    Thieme, H.R.2
  • 18
    • 0035820841 scopus 로고    scopus 로고
    • Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods
    • DOI 10.1098/rspb.2001.1599
    • A.L. Lloyd, and D.J.D. Earn Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods Proc. R. Soc. B 238 2001 985 993 (Pubitemid 32453390)
    • (2001) Proceedings of the Royal Society B: Biological Sciences , vol.268 , Issue.1470 , pp. 985-993
    • Lloyd, A.L.1
  • 19
    • 0035856957 scopus 로고    scopus 로고
    • Travelling waves and spatial hierarchies in measles epidemics
    • DOI 10.1038/414716a
    • B. Grenfell, O. Bjornstad, and J. Kappey Travelling waves and spatial hierarchies in measles epidemics Nature 414 2001 716 723 (Pubitemid 34000763)
    • (2001) Nature , vol.414 , Issue.6865 , pp. 716-723
    • Grenfell, B.T.1    Bjornstad, O.N.2    Kappey, J.3
  • 21
    • 0037426792 scopus 로고    scopus 로고
    • Modelling vaccination strategies against foot-and-mouth disease
    • DOI 10.1038/nature01343
    • M.J. Keeling, M.E.J. Woolhouse, R.M. May, G. Davies, and B.T. Grenfell Modelling vaccination strategies against foot-and-mouth disease Nature 421 2003 136 142 (Pubitemid 36090974)
    • (2003) Nature , vol.421 , Issue.6919 , pp. 136-142
    • Keeling, M.J.1    Woolhouse, M.E.J.2    May, R.M.3    Davies, G.4    Grenfell, B.T.5
  • 25
    • 0016135893 scopus 로고
    • Geographic and temporal development of plagues
    • J.V. Noble Geographic and temporal development of plagues Nature 250 1974 726 728
    • (1974) Nature , vol.250 , pp. 726-728
    • Noble, J.V.1
  • 27
    • 0030318519 scopus 로고    scopus 로고
    • Analysis of an SEIRS epidemic model with two delays
    • K.L. Cooke, and P. van den Driessche Analysis of an SEIRS epidemic model with two delays J. Math. Biol. 35 1996 240 260
    • (1996) J. Math. Biol. , vol.35 , pp. 240-260
    • Cooke, K.L.1    Van Den Driessche, P.2
  • 29
    • 38049009460 scopus 로고    scopus 로고
    • Pattern formation in a spatial S - I model with non-linear incidence rates
    • G. Sun, Z. Jin, Q.-X. Liu, and L. Li Pattern formation in a spatial S - I model with non-linear incidence rates J. Stat. Mech. Theory Exp. 11 2007 p11011
    • (2007) J. Stat. Mech. Theory Exp. , vol.11 , pp. 11011
    • Sun, G.1    Jin, Z.2    Liu, Q.-X.3    Li, L.4
  • 30
    • 77649232218 scopus 로고    scopus 로고
    • Influence of infection rate and migration on extinction of disease in spatial epidemics
    • G. Sun, Q.-X. Liu, Z. Jin, A. Chakraborty, and B. Li Influence of infection rate and migration on extinction of disease in spatial epidemics J. Theoret. Biol. 264 2010 95 103
    • (2010) J. Theoret. Biol. , vol.264 , pp. 95-103
    • Sun, G.1    Liu, Q.-X.2    Jin, Z.3    Chakraborty, A.4    Li, B.5
  • 31
    • 46749116021 scopus 로고    scopus 로고
    • Emergence of strange spatial pattern in a spatial epidemic model
    • G. Sun, Z. Jin, Q.-X. Liu, and L. Li Emergence of strange spatial pattern in a spatial epidemic model Chin. Phys. Lett. 25 2008 2296 2299
    • (2008) Chin. Phys. Lett. , vol.25 , pp. 2296-2299
    • Sun, G.1    Jin, Z.2    Liu, Q.-X.3    Li, L.4
  • 32
    • 51349145145 scopus 로고    scopus 로고
    • Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate
    • G. Sun, Z. Jin, Q.-X. Liu, and L. Li Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate J. Stat. Mech. Theory Exp. 8 2008 P08011
    • (2008) J. Stat. Mech. Theory Exp. , vol.8 , pp. 08011
    • Sun, G.1    Jin, Z.2    Liu, Q.-X.3    Li, L.4
  • 33
    • 65249093105 scopus 로고    scopus 로고
    • Spatial pattern in an epidemic system with cross-diffusion of the susceptible
    • G. Sun, Z. Jin, Q.-X. Liu, and L. Li Spatial pattern in an epidemic system with cross-diffusion of the susceptible J. Biol. Syst. 17 2009 141 152
    • (2009) J. Biol. Syst. , vol.17 , pp. 141-152
    • Sun, G.1    Jin, Z.2    Liu, Q.-X.3    Li, L.4
  • 35
    • 84863981344 scopus 로고    scopus 로고
    • Pattern formation of an epidemic model with diffusion
    • G. Sun Pattern formation of an epidemic model with diffusion Nonlinear Dynam. 69 2012 1097 1104
    • (2012) Nonlinear Dynam. , vol.69 , pp. 1097-1104
    • Sun, G.1
  • 36
    • 84897722526 scopus 로고    scopus 로고
    • Pattern formation of an epidemic model with time delay
    • J. Li, G.-Q. Sun, and Z. Jin Pattern formation of an epidemic model with time delay Physica A 403 2014 100 109
    • (2014) Physica A , vol.403 , pp. 100-109
    • Li, J.1    Sun, G.-Q.2    Jin, Z.3
  • 37
    • 0022649243 scopus 로고
    • Pattern sensitivity to boundary and initial conditions in reaction-diffusion models
    • P. Arcuri, and J.D. Murray Pattern sensitivity to boundary and initial conditions in reaction-diffusion models J. Math. Biol. 24 1986 141 165 (Pubitemid 16093705)
    • (1986) Journal of Mathematical Biology , vol.24 , Issue.2 , pp. 141-165
    • Arcuri, P.1    Murray, J.D.2
  • 40
    • 70449373358 scopus 로고    scopus 로고
    • Time-delay-induced instabilities in reaction-diffusion systems
    • S. Sen, P. Ghosh, S. Riaz, and D. Ray Time-delay-induced instabilities in reaction-diffusion systems Phys. Rev. E 80 2009 046212
    • (2009) Phys. Rev. e , vol.80 , pp. 046212
    • Sen, S.1    Ghosh, P.2    Riaz, S.3    Ray, D.4
  • 41
    • 79961118458 scopus 로고    scopus 로고
    • Control of the Hopf-Turing transition by time-delayed global feedback in a reaction-diffusion system
    • P. Ghosh Control of the Hopf-Turing transition by time-delayed global feedback in a reaction-diffusion system Phys. Rev. E 84 2011 016222
    • (2011) Phys. Rev. e , vol.84 , pp. 016222
    • Ghosh, P.1
  • 42
    • 33947514402 scopus 로고    scopus 로고
    • Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in Matlab
    • DOI 10.1007/s11538-006-9062-3
    • M. Garvie Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB Bull. Math. Biol. 69 2007 931 956 (Pubitemid 46466303)
    • (2007) Bulletin of Mathematical Biology , vol.69 , Issue.3 , pp. 931-956
    • Garvie, M.R.1
  • 44
    • 70350492526 scopus 로고    scopus 로고
    • Predicting undetected infections during the 2007 foot-and-mouth disease outbreak
    • C.P. Jewell, M.J. Keeling, and G.O. Roberts Predicting undetected infections during the 2007 foot-and-mouth disease outbreak J. R. Soc. Interface 6 2008 1145 1151
    • (2008) J. R. Soc. Interface , vol.6 , pp. 1145-1151
    • Jewell, C.P.1    Keeling, M.J.2    Roberts, G.O.3
  • 45
    • 80051671700 scopus 로고    scopus 로고
    • Periodicity and synchronization in blood-stage malaria infection
    • Y. Su, S.G. Ruan, and J.J. Wei Periodicity and synchronization in blood-stage malaria infection J. Math. Biol. 63 2011 557 574
    • (2011) J. Math. Biol. , vol.63 , pp. 557-574
    • Su, Y.1    Ruan, S.G.2    Wei, J.J.3
  • 46
    • 0033546065 scopus 로고    scopus 로고
    • Regular and irregular patterns in semiarid vegetation
    • C.A. Klausmeier Regular and irregular patterns in semiarid vegetation J. Math. Biol. 284 1999 1826 1828
    • (1999) J. Math. Biol. , vol.284 , pp. 1826-1828
    • Klausmeier, C.A.1
  • 49
    • 0036293882 scopus 로고    scopus 로고
    • Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment
    • J. Fort, and V. Mendez Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment Rep. Progr. Phys. 65 2002 895 954
    • (2002) Rep. Progr. Phys. , vol.65 , pp. 895-954
    • Fort, J.1    Mendez, V.2
  • 51
    • 0001494541 scopus 로고
    • Three types of matrix stability
    • G.W. Cross Three types of matrix stability Linear Algebra Appl. 20 1978 253 263
    • (1978) Linear Algebra Appl. , vol.20 , pp. 253-263
    • Cross, G.W.1
  • 53
    • 13544267423 scopus 로고    scopus 로고
    • Some remarks on matrix stability with application to Turing instability
    • DOI 10.1016/j.laa.2004.04.003, PII S0024379504001570, Matrices and Mathematical Biology
    • R.A. Satnoianu, and P. van den Driessche Some remarks on matrix stability with application to turing instability Linear Algebra Appl. 398 2005 69 74 (Pubitemid 40220037)
    • (2005) Linear Algebra and Its Applications , vol.398 , Issue.1-3 , pp. 69-74
    • Satnoianu, R.A.1    Van Den Driessche, P.2
  • 55
    • 2442680316 scopus 로고    scopus 로고
    • Pattern formation and spatial correlation induced by the noise in two competing species
    • D. Valenti, A. Fiasconaro, and B. Spagnolo Pattern formation and spatial correlation induced by the noise in two competing species Acta Phys. Polon. B 35 2004 1481 1489
    • (2004) Acta Phys. Polon. B , vol.35 , pp. 1481-1489
    • Valenti, D.1    Fiasconaro, A.2    Spagnolo, B.3
  • 56
    • 2442707787 scopus 로고    scopus 로고
    • Nonmonotonic behaviour of spatiotemporal pattern formation in a noisy Lotka-Volterra system
    • A. Fiasconaro, D. Valenti, and B. Spagnolo Nonmonotonic behaviour of spatiotemporal pattern formation in a noisy Lotka-Volterra system Acta Phys. Polon. B 35 2004 1491 1500
    • (2004) Acta Phys. Polon. B , vol.35 , pp. 1491-1500
    • Fiasconaro, A.1    Valenti, D.2    Spagnolo, B.3
  • 57
  • 58
    • 80052230183 scopus 로고    scopus 로고
    • Stability in a system subject to noise with regulated periodicity
    • O. Chichigina, A.A. Dubkov, D. Valenti, and B. Spagnolo Stability in a system subject to noise with regulated periodicity Phys. Rev. E 84 2011 021134
    • (2011) Phys. Rev. e , vol.84 , pp. 021134
    • Chichigina, O.1    Dubkov, A.A.2    Valenti, D.3    Spagnolo, B.4
  • 59
    • 77249116130 scopus 로고    scopus 로고
    • Rich dynamics in a predator-prey model with both noise and periodic force
    • G.-Q. Sun, Z. Jin, Q.-X. Liu, and B.L. Li Rich dynamics in a predator-prey model with both noise and periodic force BioSystems 100 2010 14 22
    • (2010) BioSystems , vol.100 , pp. 14-22
    • Sun, G.-Q.1    Jin, Z.2    Liu, Q.-X.3    Li, B.L.4
  • 60
    • 0035443952 scopus 로고    scopus 로고
    • Noise-enhanced stability of periodically driven metastable states
    • N.V. Agudov, and B. Spagnolo Noise-enhanced stability of periodically driven metastable states Phys. Rev. E 64 2001 035102(R)
    • (2001) Phys. Rev. e , vol.64
    • Agudov, N.V.1    Spagnolo, B.2
  • 61
    • 0037112845 scopus 로고    scopus 로고
    • Role of the noise on the transient dynamics of an ecosystem of interacting species
    • DOI 10.1016/S0378-4371(02)01245-1, PII S0378437102012451
    • B. Spagnolo, and A. La Barbera Role of the noise on the transient dynamics of an ecosystem of interacting species Physica A 315 2002 114 124 (Pubitemid 35412052)
    • (2002) Physica A: Statistical Mechanics and its Applications , vol.315 , Issue.1-2 , pp. 114-124
    • Spagnolo, B.1    La Barbera, A.2
  • 62
    • 0242607004 scopus 로고    scopus 로고
    • Stochastic resonance and noise delayed extinction in a model of two competing species
    • D. Valenti, A. Fiasconaro, and B. Spagnolo Stochastic resonance and noise delayed extinction in a model of two competing species Physica A 315 2004 477 486
    • (2004) Physica A , vol.315 , pp. 477-486
    • Valenti, D.1    Fiasconaro, A.2    Spagnolo, B.3


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