메뉴 건너뛰기




Volumn 362, Issue 2, 2010, Pages 286-300

Global stability of a generalized epidemic model

Author keywords

Average Lyapunov function theorem; Competitive exclusion; Globally asymptotically stable; SIRS model

Indexed keywords


EID: 70350346048     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.07.059     Document Type: Article
Times cited : (8)

References (30)
  • 1
    • 2442617064 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size
    • Ackleh A.S., and Allen L.J.S. Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size. J. Math. Biol. 147 (2003) 153-168
    • (2003) J. Math. Biol. , vol.147 , pp. 153-168
    • Ackleh, A.S.1    Allen, L.J.S.2
  • 2
    • 18144419366 scopus 로고    scopus 로고
    • Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality
    • Ackleh A.S., and Allen L.J.S. Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality. Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 175-188
    • (2005) Discrete Contin. Dyn. Syst. Ser. B , vol.5 , pp. 175-188
    • Ackleh, A.S.1    Allen, L.J.S.2
  • 4
    • 0029557912 scopus 로고
    • Pathogen coexistence induced by density-dependent host mortality
    • Andreasen V., and Pugliese A. Pathogen coexistence induced by density-dependent host mortality. J. Theoret. Biol. 177 (1995) 159-165
    • (1995) J. Theoret. Biol. , vol.177 , pp. 159-165
    • Andreasen, V.1    Pugliese, A.2
  • 5
    • 8344229974 scopus 로고    scopus 로고
    • On a basic model of a two-disease epidemic
    • Blyuss K.B., and Kyrychko Y.N. On a basic model of a two-disease epidemic. Appl. Math. Comput. 160 (2005) 177-187
    • (2005) Appl. Math. Comput. , vol.160 , pp. 177-187
    • Blyuss, K.B.1    Kyrychko, Y.N.2
  • 6
    • 0024572669 scopus 로고
    • A competitive exclusion principle for pathogen virulence
    • Bremermann H.J., and Thieme H.R. A competitive exclusion principle for pathogen virulence. J. Math. Biol. 27 (1989) 179-190
    • (1989) J. Math. Biol. , vol.27 , pp. 179-190
    • Bremermann, H.J.1    Thieme, H.R.2
  • 7
    • 38249022501 scopus 로고
    • Repellers in systems with infinite delay
    • Burton T., and Hutson V. Repellers in systems with infinite delay. J. Math. Anal. Appl. 137 (1989) 240-263
    • (1989) J. Math. Anal. Appl. , vol.137 , pp. 240-263
    • Burton, T.1    Hutson, V.2
  • 8
    • 0030128038 scopus 로고    scopus 로고
    • Competitive exclusion in gonorrhea models and other sexually transmitted disease
    • Castillo-Chavez C., Huang W., and Li J. Competitive exclusion in gonorrhea models and other sexually transmitted disease. SIAM J. Appl. Math. 56 (1996) 494-508
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 494-508
    • Castillo-Chavez, C.1    Huang, W.2    Li, J.3
  • 9
    • 0031131720 scopus 로고    scopus 로고
    • The effect of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases
    • Castillo-Chavez C., Huang W., and Li J. The effect of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases. J. Math. Biol. 35 (1997) 503-522
    • (1997) J. Math. Biol. , vol.35 , pp. 503-522
    • Castillo-Chavez, C.1    Huang, W.2    Li, J.3
  • 10
    • 0033356422 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence of multiple strains in an SIS STD model
    • Castillo-Chavez C., Huang W., and Li J. Competitive exclusion and coexistence of multiple strains in an SIS STD model. SIAM J. Appl. Math. 59 (1999) 1790-1811
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 1790-1811
    • Castillo-Chavez, C.1    Huang, W.2    Li, J.3
  • 11
    • 0031154662 scopus 로고    scopus 로고
    • To treat or not to treat: The case of tuberculosis
    • Castillo-Chavez C., and Feng Z. To treat or not to treat: The case of tuberculosis. J. Math. Biol. 35 (1997) 629-656
    • (1997) J. Math. Biol. , vol.35 , pp. 629-656
    • Castillo-Chavez, C.1    Feng, Z.2
  • 12
    • 84972551554 scopus 로고
    • On the asymptotic behavior of solutions of certain non-autonomous differential equations
    • Hara T. On the asymptotic behavior of solutions of certain non-autonomous differential equations. Osaka J. Math. 12 (1975) 267-282
    • (1975) Osaka J. Math. , vol.12 , pp. 267-282
    • Hara, T.1
  • 13
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious disease
    • Hethcote H.W. The mathematics of infectious disease. SIAM J. Appl. Math. 42 (2000) 599-653
    • (2000) SIAM J. Appl. Math. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 14
    • 0001862504 scopus 로고
    • A unified approach to persistence
    • Hofbauer J. A unified approach to persistence. Acta Appl. Math. 14 (1989) 11-22
    • (1989) Acta Appl. Math. , vol.14 , pp. 11-22
    • Hofbauer, J.1
  • 15
    • 84966222841 scopus 로고
    • Uniform persistence and repellors for maps
    • Hofbauer J., and So J.W.H. Uniform persistence and repellors for maps. Proc. Amer. Math. Soc. 107 (1989) 1137-1142
    • (1989) Proc. Amer. Math. Soc. , vol.107 , pp. 1137-1142
    • Hofbauer, J.1    So, J.W.H.2
  • 16
    • 0001439703 scopus 로고
    • A theorem on average Liapunov functions
    • Hutson V. A theorem on average Liapunov functions. Monatsh. Math. 98 (1984) 267-275
    • (1984) Monatsh. Math. , vol.98 , pp. 267-275
    • Hutson, V.1
  • 17
    • 34147148647 scopus 로고    scopus 로고
    • Avian-human influenza epidemic model
    • Iwami S., Takeuchi Y., and Liu X. Avian-human influenza epidemic model. Math. Biosci. 207 (2007) 1-25
    • (2007) Math. Biosci. , vol.207 , pp. 1-25
    • Iwami, S.1    Takeuchi, Y.2    Liu, X.3
  • 18
    • 0035426229 scopus 로고    scopus 로고
    • Permanence of host-parasitoid systems
    • Kon R., and Takeuchi Y. Permanence of host-parasitoid systems. Nonlinear Anal. 47 (2001) 1383-1393
    • (2001) Nonlinear Anal. , vol.47 , pp. 1383-1393
    • Kon, R.1    Takeuchi, Y.2
  • 19
    • 35448954985 scopus 로고    scopus 로고
    • Single-class orbits in nonlinear Leslie matrix models for semelparous populations
    • Kon R., and Iwasa Y. Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol. 55 (2007) 781-802
    • (2007) J. Math. Biol. , vol.55 , pp. 781-802
    • Kon, R.1    Iwasa, Y.2
  • 20
    • 34248213096 scopus 로고    scopus 로고
    • Permanence of structured population models governed by ODEs and the basic reproduction number
    • Kon R. Permanence of structured population models governed by ODEs and the basic reproduction number. Japan J. Indust. Appl. Math. 24 (2007) 17-37
    • (2007) Japan J. Indust. Appl. Math. , vol.24 , pp. 17-37
    • Kon, R.1
  • 21
    • 31244431623 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models
    • Korobeinikov A., and Wake G.C. Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models. Appl. Math. Lett. 15 (2002) 955-960
    • (2002) Appl. Math. Lett. , vol.15 , pp. 955-960
    • Korobeinikov, A.1    Wake, G.C.2
  • 22
    • 1342310609 scopus 로고    scopus 로고
    • Coexistence of pathogens in sexually-transmitted disease models
    • Li J., Ma Z., Blythe S.P., and Castillo-Chavez C. Coexistence of pathogens in sexually-transmitted disease models. J. Math. Biol. 47 (2003) 547-568
    • (2003) J. Math. Biol. , vol.47 , pp. 547-568
    • Li, J.1    Ma, Z.2    Blythe, S.P.3    Castillo-Chavez, C.4
  • 24
    • 0021085051 scopus 로고
    • Epidemiology and genetics in the coevolution of parasites and hosts
    • May R.M., and Anderson R.M. Epidemiology and genetics in the coevolution of parasites and hosts. Proc. R. Soc. Lond. B 219 (1983) 281-313
    • (1983) Proc. R. Soc. Lond. B , vol.219 , pp. 281-313
    • May, R.M.1    Anderson, R.M.2
  • 26
    • 0036238636 scopus 로고    scopus 로고
    • On the evolutionary coexistence of parasite strains
    • Pugliese A. On the evolutionary coexistence of parasite strains. Math. Biosci. 178 (2002) 355-375
    • (2002) Math. Biosci. , vol.178 , pp. 355-375
    • Pugliese, A.1
  • 27
    • 38749140744 scopus 로고    scopus 로고
    • Pathogen competition and coexistence and the evolution of virulence
    • Takeuchi Y., Iwasa Y., and Sato K. (Eds), Springer
    • Thieme H.R. Pathogen competition and coexistence and the evolution of virulence. In: Takeuchi Y., Iwasa Y., and Sato K. (Eds). Mathematics for Life Sciences and Medicine (2007), Springer
    • (2007) Mathematics for Life Sciences and Medicine
    • Thieme, H.R.1
  • 28
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29-48
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 29
    • 25844432297 scopus 로고    scopus 로고
    • Competition of pathogen strains leading to infection with variable infectivity and the effect of treatment
    • Xiridou M., Kretzschmar M., and Geskus R. Competition of pathogen strains leading to infection with variable infectivity and the effect of treatment. Math. Biosci. 197 (2005) 153-172
    • (2005) Math. Biosci. , vol.197 , pp. 153-172
    • Xiridou, M.1    Kretzschmar, M.2    Geskus, R.3
  • 30
    • 33846561621 scopus 로고    scopus 로고
    • Global stability of a delayed SIR epidemic model with density dependent birth and death rates
    • Yoshida N., and Hara T. Global stability of a delayed SIR epidemic model with density dependent birth and death rates. J. Comput. Appl. Math. 47 201 (2007) 339-347
    • (2007) J. Comput. Appl. Math. , vol.47 , Issue.201 , pp. 339-347
    • Yoshida, N.1    Hara, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.