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Volumn 71, Issue 1, 2011, Pages 147-168

A nonlocal and time-delayed reaction-diffusion model of dengue transmission

Author keywords

Basic reproduction number; Dengue transmission; Spatial diffusion; Threshold dynamics; Time delays

Indexed keywords

ASYMPTOTICALLY STABLE; BASIC REPRODUCTION NUMBER; DENGUE TRANSMISSION; DENGUE VIRUS; DIFFUSION COEFFICIENTS; DISEASE-FREE EQUILIBRIUM; EXPLICIT FORMULA; INCUBATION PERIODS; MODEL SYSTEM; NONLOCAL; NUMERICAL SIMULATION; REACTION-DIFFUSION MODELS; SPATIAL DIFFUSION; THRESHOLD DYNAMICS;

EID: 79952343940     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090775890     Document Type: Article
Times cited : (168)

References (28)
  • 1
    • 0025132577 scopus 로고
    • A time-delay model of single-species growth with stage structure
    • DOI 10.1016/0025-5564(90)90019-U
    • W. G. Aiello and H. I. Freedman, A time delay model of single-species growth with stage structure, Math. Biosci., 101 (1990), pp. 139-153. (Pubitemid 20357965)
    • (1990) Mathematical Biosciences , vol.101 , Issue.2 , pp. 139-153
    • Aiello, W.G.1    Freedman, H.I.2
  • 2
    • 44449127242 scopus 로고    scopus 로고
    • Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
    • L. J. S. Allen, B. M. Bolker, Y. Lou, and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst., 21 (2008), pp. 1-20.
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , pp. 1-20
    • Allen, L.J.S.1    Bolker, B.M.2    Lou, Y.3    Nevai, A.L.4
  • 3
    • 84873708581 scopus 로고    scopus 로고
    • Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease
    • J. Arino, C. Bowman, A. Gumel, and S. Portet, Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease, J. Biol. Dyn., 1 (2007), pp. 32-343.
    • (2007) J. Biol. Dyn. , vol.1 , pp. 32-343
    • Arino, J.1    Bowman, C.2    Gumel, A.3    Portet, S.4
  • 4
    • 21444451814 scopus 로고    scopus 로고
    • A mathematical model for assessing control strategies against West Nile virus
    • DOI 10.1016/j.bulm.2005.01.002, PII S0092824005000091
    • C. Bowman, A. B. Gumel, P. van den Drissche, J. Wu, and H. Zhu, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 67 (2005), pp. 1107-1133. (Pubitemid 40912468)
    • (2005) Bulletin of Mathematical Biology , vol.67 , Issue.5 , pp. 1107-1133
    • Bowman, C.1    Gumel, A.B.2    Van Den Driessche, P.3    Wu, J.4    Zhu, H.5
  • 5
    • 0001309976 scopus 로고
    • The spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators
    • F. Chatelin, The spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators, SIAM Rev., 23 (1981), pp. 495-522.
    • (1981) SIAM Rev. , vol.23 , pp. 495-522
    • Chatelin, F.1
  • 7
    • 0025159677 scopus 로고
    • On the definition and the computation of the basic reproduction ratio R0 in the models for infectious disease in heterogeneous populations
    • O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R0 in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), pp. 365-382.
    • (1990) J. Math. Biol. , vol.28 , pp. 365-382
    • Diekmann, O.1    Heesterbeek, J.A.P.2    Metz, J.A.J.3
  • 8
    • 43049140192 scopus 로고    scopus 로고
    • On a temporal model for the Chikungunya disease: Modeling, theory and numerics
    • Y. Dumont, F. Chiroleu, and C. Domerg, On a temporal model for the Chikungunya disease: Modeling, theory and numerics, Math. Biosci., 213 (2008), pp. 80-91.
    • (2008) Math. Biosci. , vol.213 , pp. 80-91
    • Dumont, Y.1    Chiroleu, F.2    Domerg, C.3
  • 11
    • 0031137301 scopus 로고    scopus 로고
    • Competitive exclusion in a vector-host model for the dengue fever
    • Z. Feng and J. X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol., 35 (1997), pp. 523-544. (Pubitemid 127759099)
    • (1997) Journal of Mathematical Biology , vol.35 , Issue.5 , pp. 523-544
    • Feng, Z.1    Velasco-Hernandez, J.X.2
  • 12
    • 49849105967 scopus 로고    scopus 로고
    • Backward bifurcations in dengue transmission dynamics
    • S. M. Garba, A. B. Gumel, and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), pp. 11-25.
    • (2008) Math. Biosci. , vol.215 , pp. 11-25
    • Garba, S.M.1    Gumel, A.B.2    Abu Bakar, M.R.3
  • 14
  • 15
    • 67349178620 scopus 로고    scopus 로고
    • Asymptotic profiles of the positive steady state for an SIS epidemic reaction-diffusion model. I
    • R. Peng, Asymptotic profiles of the positive steady state for an SIS epidemic reaction-diffusion model. I, J. Differential Equations, 247 (2009), pp. 1096-1119.
    • (2009) J. Differential Equations , vol.247 , pp. 1096-1119
    • Peng, R.1
  • 16
    • 0003270907 scopus 로고
    • Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems
    • American Mathematical Society, Providence, RI
    • H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr. 41, American Mathematical Society, Providence, RI, 1995.
    • (1995) Math. Surveys Monogr. , vol.41
    • Smith, H.L.1
  • 18
    • 16344394631 scopus 로고    scopus 로고
    • Mathematical models for the Aedes aegypti dispersal dynamics: Travelling waves by wing and wind
    • DOI 10.1016/j.bulm.2004.08.005
    • L. T. Takahashi, N. A. Maidana, W. Castro Ferreira, Jr., P. Pulino, and H. M. Yang, Mathematical models for the Aedes aegypti dispersal dynamics: Travelling waves by wing and wind, Bull. Math. Biol., 67 (2005), pp. 509-528. (Pubitemid 40466383)
    • (2005) Bulletin of Mathematical Biology , vol.67 , Issue.3 , pp. 509-528
    • Takahashi, L.T.1    Maidana, N.A.2    Ferreira Jr., W.C.3    Pulino, P.4    Yang, H.M.5
  • 19
    • 77952672921 scopus 로고
    • Convergence results and Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
    • H. R. Thieme, Convergence results and Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), pp. 755-763.
    • (1992) J. Math. Biol. , vol.30 , pp. 755-763
    • Thieme, H.R.1
  • 20
    • 67649378819 scopus 로고    scopus 로고
    • Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity
    • H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), pp. 188-211.
    • (2009) SIAM J. Appl. Math. , vol.70 , pp. 188-211
    • Thieme, H.R.1
  • 21
    • 0035373461 scopus 로고    scopus 로고
    • A non-local delayed and diffusive predator-prey model
    • DOI 10.1016/S0362-546X(00)00112-7, PII S0362546X00001127
    • H. R. Thieme and X.-Q. Zhao, A non-local delayed and diffusive predator-prey model, Nonlinear Anal. Real World Appl., 2 (2001), pp. 145-160. (Pubitemid 33379466)
    • (2001) Nonlinear Analysis: Real World Applications , vol.2 , Issue.2 , pp. 145-160
    • Thieme, H.R.1    Zhao, X.-Q.2
  • 22
    • 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), pp. 29-48. (Pubitemid 35304346)
    • (2002) Mathematical Biosciences , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2
  • 23
    • 0028487170 scopus 로고
    • A model for Chagas disease involving transmission by vectors and blood transfusion
    • J. X. Velascohernandez, A model for Chagas disease involving transmission by vectors and blood transfusion, Theoret. Popul. Biol., 46 (1994), pp. 1-13.
    • (1994) Theoret. Popul. Biol. , vol.46 , pp. 1-13
    • Velascohernandez, J.X.1
  • 24
    • 33747178342 scopus 로고    scopus 로고
    • An epidemic model with population dispersal and infection period
    • DOI 10.1137/050622948
    • W. Wang and X.-Q. Zhao, An epidemic model with population dispersal and infection period, SIAM J. Appl. Math., 66 (2006), pp. 1454-1472. (Pubitemid 44231198)
    • (2006) SIAM Journal on Applied Mathematics , vol.66 , Issue.4 , pp. 1454-1472
    • Wang, W.1    Zhao, X.-Q.2
  • 25
    • 0003345730 scopus 로고    scopus 로고
    • Theory and applications of partial functional differential equations
    • Springer-Verlag, New York
    • J. Wu, Theory and Applications of Partial Functional Differential Equations, Appl. Math. Sci. 119, Springer-Verlag, New York, 1996.
    • (1996) Appl. Math. Sci. , vol.119
    • Wu, J.1
  • 26
    • 43749085001 scopus 로고    scopus 로고
    • A nonlocal reaction-diffusion population model with stage structure
    • D. Xu and X.-Q. Zhao, A nonlocal reaction-diffusion population model with stage structure, Can. Appl. Math. Q., 11 (2003), pp. 303-320.
    • (2003) Can. Appl. Math. Q. , vol.11 , pp. 303-320
    • Xu, D.1    Zhao, X.-Q.2
  • 27
    • 40149088447 scopus 로고    scopus 로고
    • Assessing the effects of vector control on dengue transmission
    • DOI 10.1016/j.amc.2007.08.046, PII S0096300307009101
    • H. M. Yang and C. P. Ferreira, Assessing the effects of vector control on dengue transmission, Appl. Math. Comput., 198 (2008), pp. 401-413. (Pubitemid 351329396)
    • (2008) Applied Mathematics and Computation , vol.198 , Issue.1 , pp. 401-413
    • Yang, H.M.1    Ferreira, C.P.2
  • 28
    • 79952326119 scopus 로고    scopus 로고
    • Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay
    • X.-Q. Zhao, Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay, Can. Appl. Math. Q., 17 (2009), pp. 271-281.
    • (2009) Can. Appl. Math. Q. , vol.17 , pp. 271-281
    • Zhao, X.-Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.