메뉴 건너뛰기




Volumn 136, Issue 8, 2008, Pages 2793-2802

A graph-theoretic approach to the method of global Lyapunov functions

Author keywords

Global stability; Graph theory; Lyapunov functions; Multi group epidemic models

Indexed keywords


EID: 70349388314     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-08-09341-6     Document Type: Article
Times cited : (319)

References (17)
  • 1
    • 12844261174 scopus 로고
    • Global stability results for a multigroup SIR epidemic model
    • in: T. G. Hallam, L. J. Gross, and S. A. Levin Eds., MR1040340 91c:92074
    • E. Beretta and V. Capasso, Global stability results for a multigroup SIR epidemic model, in: T. G. Hallam, L. J. Gross, and S. A. Levin (Eds.), Mathematical Ecology, World Scientific, Teaneck, NJ, 1988, pp. 317-342. MR1040340 (91c:92074)
    • (1988) Mathematical Ecology, World Scientific, Teaneck, NJ , pp. 317-342
    • Beretta, E.1    Capasso, V.2
  • 2
    • 0037520454 scopus 로고
    • Dynamical Systems: Stability Theory and Applications
    • Springer, Berlin, MR0219843 36:2917
    • N. P. Bhatia and G. P. Szegö, Dynamical Systems: Stability Theory and Applications, Lecture Notes in Mathematics, Vol. 35, Springer, Berlin, 1967. MR0219843 (36:2917)
    • (1967) Lecture Notes in Mathematics , vol.35
    • Bhatia, N.P.1    Szegö, G.P.2
  • 3
    • 0002808656 scopus 로고
    • Global stability and persistence of simple food chains
    • MR809991 87g:92040
    • H. I. Freedman and J. W.-H. So, Global stability and persistence of simple food chains, Math. Biosci. 76 (1985) 69-86. MR809991 (87g:92040)
    • (1985) Math. Biosci. , vol.76 , pp. 69-86
    • Freedman, H.I.1    So, J.W.-H.2
  • 4
    • 33847001630 scopus 로고    scopus 로고
    • Global dynamics of a staged progression model for infectious diseases
    • MR2217225 2006m:92086
    • H. Guo and M. Y. Li, Global dynamics of a staged progression model for infectious diseases, Math. Biosci. Eng. 3 (2006) 513-525. MR2217225 (2006m:92086)
    • (2006) Math. Biosci. Eng. , vol.3 , pp. 513-525
    • Guo, H.1    Li, M.Y.2
  • 5
    • 0018247773 scopus 로고
    • An immunization model for a heterogeneous population
    • MR520143 80k:92009
    • H. W. Hethcote, An immunization model for a heterogeneous population, Theor. Popu. Biol. 14 (1978) 338-349. MR520143 (80k:92009)
    • (1978) Theor. Popu. Biol. , vol.14 , pp. 338-349
    • Hethcote, H.W.1
  • 6
    • 0021984692 scopus 로고
    • Stability of the endemic equilibrium in epidemic models with subpopulations
    • MR810991 87c:92046
    • H. W. Hethcote and H. R. Thieme, Stability of the endemic equilibrium in epidemic models with subpopulations, Math. Biosci. 75 (1985) 205-227. MR810991 (87c:92046)
    • (1985) Math. Biosci. , vol.75 , pp. 205-227
    • Hethcote, H.W.1    Thieme, H.R.2
  • 7
    • 0000723140 scopus 로고
    • Stability and bifurcation for a multiplegroup model for the dynamics of HIV/AIDS transmission
    • MR1163809 93d:92009
    • W. Huang, K. L. Cooke, and C. Castillo-Chavez, Stability and bifurcation for a multiplegroup model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math. 52 (1992) 835-854. MR1163809 (93d:92009)
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 835-854
    • Huang, W.1    Cooke, K.L.2    Castillo-Chavez, C.3
  • 8
    • 0003657590 scopus 로고    scopus 로고
    • 3rd ed., Addison-Wesley, Reading, MA, MR0286317 44:3530
    • D. E. Knuth, The Art of Computer Programming, Vol. 1, 3rd ed., Addison-Wesley, Reading, MA, 1997. MR0286317 (44:3530)
    • (1997) The Art of Computer Programming , vol.1
    • Knuth, D.E.1
  • 9
    • 0035427292 scopus 로고    scopus 로고
    • A Lyapunov function for Leslie-Gower predator-prey models
    • MR1836072
    • A. Korobeinikov, A Lyapunov function for Leslie-Gower predator-prey models, Appl. Math. Lett. 14 (2001) 697-699. MR1836072
    • (2001) Appl. Math. Lett. , vol.14 , pp. 697-699
    • Korobeinikov, A.1
  • 10
    • 27244439640 scopus 로고    scopus 로고
    • A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence
    • MR2130156 2005k:92065
    • A. Korobeinikov and P. K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng. 1 (2004) 57-60. MR2130156 (2005k:92065)
    • (2004) Math. Biosci. Eng. , vol.1 , pp. 57-60
    • Korobeinikov, A.1    Maini, P.K.2
  • 11
    • 0017226769 scopus 로고
    • A deterministic model for gonorrhea in a nonhomogeneous population
    • MR0403726 53:7537
    • A. Lajmanovich and J. A. York, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28 (1976) 221-236. MR0403726 (53:7537)
    • (1976) Math. Biosci. , vol.28 , pp. 221-236
    • Lajmanovich, A.1    York, J.A.2
  • 13
    • 0009418458 scopus 로고
    • Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations
    • MR1197481 93k:92010
    • X. Lin and J. W.-H. So, Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations, J. Austral. Math. Soc. Ser. B 34 (1993) 282-295. MR1197481 (93k:92010)
    • (1993) J. Austral. Math. Soc. Ser. B , vol.34 , pp. 282-295
    • Lin, X.1    So, J.W.-H.2
  • 14
    • 77950797637 scopus 로고
    • Canadian Mathematical Congress, Montreal, MR0274333 43:98
    • J. W. Moon, Counting Label led Trees, Canadian Mathematical Congress, Montreal, 1970. MR0274333 (43:98)
    • (1970) Counting Label Led Trees
    • Moon, J.W.1
  • 15
    • 0344419318 scopus 로고
    • Local stability in epidemic models for heterogeneous populations
    • in: V. Capasso, E. Grosso, and S. L. Paveri-Fontana Eds., Springer, Berlin, MR812889
    • H. R. Thieme, Local stability in epidemic models for heterogeneous populations, in: V. Capasso, E. Grosso, and S. L. Paveri-Fontana (Eds.), Mathematics in Biology and Medicine, Lecture Notes in Biomathematics, Vol. 57, Springer, Berlin, 1985, pp. 185-189. MR812889
    • (1985) Mathematics in Biology and Medicine, Lecture Notes in Biomathematics , vol.57 , pp. 185-189
    • Thieme, H.R.1
  • 16
    • 85194307652 scopus 로고    scopus 로고
    • Princeton University Press, Princeton, NJ, MR1993355 2004m:92030
    • H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton, NJ, 2003. MR1993355 (2004m:92030)
    • (2003) Mathematics in Population Biology
    • Thieme, H.R.1
  • 17
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • MR1950747 2003m:92071
    • 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. MR1950747 (2003m:92071)
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.