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Volumn 23, Issue 2, 2010, Pages 279-292

Global stability of an epidemic model for vector-borne disease

Author keywords

Basic reproduction number; Endemic equilibrium; Epidemic model; Global stability; Vector borne disease

Indexed keywords

BASIC REPRODUCTION NUMBER; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELS; GLOBAL STABILITY; VECTOR-BORNE DISEASE;

EID: 77952411393     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-010-8436-7     Document Type: Article
Times cited : (25)

References (32)
  • 1
    • 84864173320 scopus 로고    scopus 로고
    • WHO, Malaria, 10 fact on Malaria, Available from
    • WHO, Malaria, 10 fact on Malaria, Available from: http://www. who. int/features/factfiles/malaria/en/index. html, 2009.
    • (2009)
  • 2
    • 84864168775 scopus 로고    scopus 로고
    • CDC, Available from: CDC Dengue Fever homepage
    • CDC, Available from: CDC Dengue Fever homepage, http://www. cdc. gov/ncidod/dvbid/index. htm, 2003.
    • (2003)
  • 3
    • 84864169941 scopus 로고    scopus 로고
    • CDC, West Nile virus update, current case count, Available form
    • CDC, West Nile virus update, current case count, Available form: http://www. cdc. gov/ncidod/dvbib/westnile/surv& controlCaseCount03. htm, 2003.
    • (2003)
  • 4
    • 84864173328 scopus 로고    scopus 로고
    • West Nile Virus, Available form
    • West Nile Virus, Available form: http://www. sfcdcp. org/index. cfm?id=90.
  • 5
    • 0024301014 scopus 로고    scopus 로고
    • The dynamics of vectors-transmitted diseases in human communities
    • D. J. Rogers, The dynamics of vectors-transmitted diseases in human communities, Phil. Trans. R. Soc. London B, 1998, 321: 513-528.
    • (1998) Phil. Trans. R. Soc. London B , vol.321 , pp. 513-528
    • Rogers, D.J.1
  • 6
    • 0034410937 scopus 로고    scopus 로고
    • Why model malaria?
    • F. E. Mckenzie, Why model malaria? Parasitol Today, 2000, 16: 511-516.
    • (2000) Parasitol Today , vol.16 , pp. 511-516
    • McKenzie, F.E.1
  • 7
    • 2542449374 scopus 로고    scopus 로고
    • A mathematical model for Chagas disease with infection-age-dependent infectivity
    • H. Inaba and H. Sekine, A mathematical model for Chagas disease with infection-age-dependent infectivity, Math. Biosci., 2004, 190: 39-69.
    • (2004) Math. Biosci. , vol.190 , pp. 39-69
    • Inaba, H.1    Sekine, H.2
  • 8
    • 1642327086 scopus 로고    scopus 로고
    • Coupling ecology and evolution: Malaria and the S-gene across time scales
    • Z. Feng, D. L. Smith, F. E. McKenzie, S. A. Levin, Coupling ecology and evolution: Malaria and the S-gene across time scales, Math. Biosci., 2004, 189: 1-19.
    • (2004) Math. Biosci. , vol.189 , pp. 1-19
    • Feng, Z.1    Smith, D.L.2    Mckenzie, F.E.3    Levin, S.A.4
  • 10
    • 21444451814 scopus 로고    scopus 로고
    • A mathematical model for assessing control strategies against West Nile virus
    • C. Bowman, A. B. Gumel, P. van den Driessche, J. Wu, and H. Zhu, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 2005, 67: 1107-1121.
    • (2005) Bull. Math. Biol. , vol.67 , pp. 1107-1121
    • Bowman, C.1    Gumel, A.B.2    van den Driessche, P.3    Wu, J.4    Zhu, H.5
  • 11
    • 0027086839 scopus 로고
    • A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics
    • E. A. Newton and P. Reiter, A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics, Am. J. Trop. Med. Hyg., 1992, 47: 709-720.
    • (1992) Am. J. Trop. Med. Hyg. , vol.47 , pp. 709-720
    • Newton, E.A.1    Reiter, P.2
  • 12
    • 0032526469 scopus 로고    scopus 로고
    • Analysis of a dengue disease transmission model
    • L. Esteva and C. Vargas, Analysis of a dengue disease transmission model, Math. Biosci., 1998, 150: 131-151.
    • (1998) Math. Biosci. , vol.150 , pp. 131-151
    • Esteva, L.1    Vargas, C.2
  • 13
    • 0031137301 scopus 로고    scopus 로고
    • Competitive exclusion in a vector-host model for the dengue virus
    • Z. Feng and J. X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue virus, J. Math. Biol., 1997, 35: 523-544.
    • (1997) J. Math. Biol. , vol.35 , pp. 523-544
    • Feng, Z.1    Velasco-Hernandez, J.X.2
  • 14
    • 0033089022 scopus 로고    scopus 로고
    • A model for dengue disease with variable human population
    • L. Esteva and C. Vargas, A model for dengue disease with variable human population, J. Math. Biol., 1999, 38: 220-236.
    • (1999) J. Math. Biol. , vol.38 , pp. 220-236
    • Esteva, L.1    Vargas, C.2
  • 15
    • 0018656345 scopus 로고
    • Population biology of infectious diseases: Part 1
    • R. M. Aderson and R. M. May, Population biology of infectious diseases: Part 1, Nature, 1979, 280: 361-368.
    • (1979) Nature , vol.280 , pp. 361-368
    • Aderson, R.M.1    May, R.M.2
  • 16
    • 0017228276 scopus 로고
    • Qualitative analysis of communicable disease models
    • H. W. Hethcote, Qualitative analysis of communicable disease models, Math. Biosci., 1976, 28: 335-356.
    • (1976) Math. Biosci. , vol.28 , pp. 335-356
    • Hethcote, H.W.1
  • 17
    • 0030544879 scopus 로고    scopus 로고
    • A geometric approach to global-stability problems
    • M. Y. Li and J. S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal., 1996, 27: 1070-1083.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1070-1083
    • Li, M.Y.1    Muldowney, J.S.2
  • 20
    • 0002231761 scopus 로고
    • A brief survey of persistence
    • S. Busenberg and M. Martelli (Eds.), New York: Springer
    • P. Waltman, A brief survey of persistence, in: S. Busenberg, M. Martelli (Eds.), Delay Differential Equations and Dynamical Systems, Springer, New York, 1991, 31-45.
    • (1991) Delay Differential Equations and Dynamical Systems , pp. 31-45
    • Waltman, P.1
  • 21
    • 0000361466 scopus 로고
    • Uniform persistence and flows near a closed positively invariant set
    • H. I. Freedman, M. X. Tang, and S. G. Ruan, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Diff. Equ., 1994, 6: 583-601.
    • (1994) J. Dynam. Diff. Equ. , vol.6 , pp. 583-601
    • Freedman, H.I.1    Tang, M.X.2    Ruan, S.G.3
  • 22
    • 0032812296 scopus 로고    scopus 로고
    • Global dynamics of an SEIR model with a varying total population size
    • M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, Global dynamics of an SEIR model with a varying total population size, Math. Biosci., 1999, 160: 191-213.
    • (1999) Math. Biosci. , vol.160 , pp. 191-213
    • Li, M.Y.1    Graef, J.R.2    Wang, L.3    Karsai, J.4
  • 23
    • 84971128384 scopus 로고
    • Some applications of Hausdorff dimension inequalities for orinary differential equations
    • R. A. Smith, Some applications of Hausdorff dimension inequalities for orinary differential equations, Proc. R. Soc. Edinburgh A, 1986, 104: 235-251.
    • (1986) Proc. R. Soc. Edinburgh A , vol.104 , pp. 235-251
    • Smith, R.A.1
  • 24
    • 0000147071 scopus 로고
    • On R. A. Smith's autonomous convergence theorem
    • M. Y. Li and J. S. Muldowney, On R. A. Smith's autonomous convergence theorem, Rocky Mount. J. Math., 1995, 25: 365-379.
    • (1995) Rocky Mount. J. Math. , vol.25 , pp. 365-379
    • Li, M.Y.1    Muldowney, J.S.2
  • 26
    • 84972090819 scopus 로고
    • Systems of differential equations that are competitive or coopertitive. VI: A local C'closing lemma for 3-dimensional systems
    • M. W. Hirsch, Systems of differential equations that are competitive or coopertitive. VI: A local C'closing lemma for 3-dimensional systems, Ergod. Theor. Dynam. Sys., 1991, 11: 443-454.
    • (1991) Ergod. Theor. Dynam. Sys. , vol.11 , pp. 443-454
    • Hirsch, M.W.1
  • 27
    • 0001703398 scopus 로고
    • Am improved closing lemma and a general density theorem
    • C. C. Pugh, Am improved closing lemma and a general density theorem, Am. J. Math., 1967, 89: 1010-1021.
    • (1967) Am. J. Math. , vol.89 , pp. 1010-1021
    • Pugh, C.C.1
  • 30
    • 0016027180 scopus 로고
    • Logarithmic norms and projections applied to linear differential systems
    • R. H. Martin Jr., Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl., 1974, 45: 392-410.
    • (1974) J. Math. Anal. Appl. , vol.45 , pp. 392-410
    • Martin Jr., R.H.1
  • 31
    • 0001172085 scopus 로고
    • Additive compound matrices and inequality for eigenvalues of stochastic matrices
    • M. Fiedler, Additive compound matrices and inequality for eigenvalues of stochastic matrices, Czech Math. J., 1974, 99: 392-402.
    • (1974) Czech Math. J. , vol.99 , pp. 392-402
    • Fiedler, M.1
  • 32
    • 84880990802 scopus 로고
    • Compound matrices and ordinary differential equations
    • J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mount. J. Math., 1990, 20: 857-872.
    • (1990) Rocky Mount. J. Math. , vol.20 , pp. 857-872
    • Muldowney, J.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.