메뉴 건너뛰기




Volumn 410, Issue 2, 2014, Pages 719-732

Complete global analysis of an SIRS epidemic model with graded cure and incomplete recovery rates

Author keywords

Cure rate; Global asymptotic stability; Lyapunov functional; SIRS epidemic model

Indexed keywords


EID: 84885315493     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2013.08.024     Document Type: Article
Times cited : (54)

References (32)
  • 2
    • 84859101715 scopus 로고    scopus 로고
    • Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
    • Enatsu Y., Nakata Y., Muroya Y. Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model. Nonlinear Anal. Real World Appl. 2012, 13:2120-2133.
    • (2012) Nonlinear Anal. Real World Appl. , vol.13 , pp. 2120-2133
    • Enatsu, Y.1    Nakata, Y.2    Muroya, Y.3
  • 3
    • 26444475399 scopus 로고    scopus 로고
    • Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence
    • Gomes M.G.M., Margheri A., Medley G.F., Rebelo E.C. Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence. J. Math. Biol. 2005, 51:414-430.
    • (2005) J. Math. Biol. , vol.51 , pp. 414-430
    • Gomes, M.G.M.1    Margheri, A.2    Medley, G.F.3    Rebelo, E.C.4
  • 4
    • 1642350077 scopus 로고    scopus 로고
    • Infection, reinfection and vaccination under sub-optimal immune protection: epidemiological perspectives
    • Gomes M.G.M., White L.J., Medley G.F. Infection, reinfection and vaccination under sub-optimal immune protection: epidemiological perspectives. J. Theoret. Biol. 2004, 228:539-549.
    • (2004) J. Theoret. Biol. , vol.228 , pp. 539-549
    • Gomes, M.G.M.1    White, L.J.2    Medley, G.F.3
  • 5
    • 78651226178 scopus 로고    scopus 로고
    • Bifurcations of an SIRS epidemic model with nonlinear incidence rate
    • Hu Z., Bi P., Ma W., Ruan S. Bifurcations of an SIRS epidemic model with nonlinear incidence rate. Discrete Contin. Dyn. Syst. Ser. B 2011, 15:93-112.
    • (2011) Discrete Contin. Dyn. Syst. Ser. B , vol.15 , pp. 93-112
    • Hu, Z.1    Bi, P.2    Ma, W.3    Ruan, S.4
  • 6
    • 84876673855 scopus 로고    scopus 로고
    • A note on global stability for a heroin epidemic model with distributed delay
    • Huang G., Liu A. A note on global stability for a heroin epidemic model with distributed delay. Appl. Math. Lett. 2013, 26:687-691.
    • (2013) Appl. Math. Lett. , vol.26 , pp. 687-691
    • Huang, G.1    Liu, A.2
  • 7
    • 69049101951 scopus 로고    scopus 로고
    • Dynamics of a delayed epidemic model with non-monotonic incidence rate
    • Huo H.-F., Ma Z.-P. Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun. Nonlinear Sci. Numer. Simul. 2010, 15:459-468.
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 459-468
    • Huo, H.-F.1    Ma, Z.-P.2
  • 8
    • 34250220630 scopus 로고    scopus 로고
    • An SIRS model with a nonlinear incidence rate
    • Jin Y., Wang W., Xiao S. An SIRS model with a nonlinear incidence rate. Chaos Solitons Fractals 2007, 34:1482-1497.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1482-1497
    • Jin, Y.1    Wang, W.2    Xiao, S.3
  • 9
    • 34547655762 scopus 로고    scopus 로고
    • Global properties of infectious disease models with nonlinear incidence
    • Korobeinikov A. Global properties of infectious disease models with nonlinear incidence. Bull. Math. Biol. 2007, 69:1871-1886.
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1871-1886
    • Korobeinikov, A.1
  • 10
    • 79957546402 scopus 로고    scopus 로고
    • Global behaviour of a heroin epidemic model with distributed delays
    • Liu J., Zhang T. Global behaviour of a heroin epidemic model with distributed delays. Appl. Math. Lett. 2011, 24:1685-1692.
    • (2011) Appl. Math. Lett. , vol.24 , pp. 1685-1692
    • Liu, J.1    Zhang, T.2
  • 11
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • Liu W.M., Levin S.A., Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 1986, 23:187-204.
    • (1986) J. Math. Biol. , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 12
    • 0030277612 scopus 로고    scopus 로고
    • Multiparametric bifurcations for a model in epidemiology
    • Lizana M., Rivero J. Multiparametric bifurcations for a model in epidemiology. J. Math. Biol. 1996, 35:21-36.
    • (1996) J. Math. Biol. , vol.35 , pp. 21-36
    • Lizana, M.1    Rivero, J.2
  • 14
    • 70350722240 scopus 로고    scopus 로고
    • Complete global stability for an SIR epidemic model with delay-Distributed or discrete
    • McCluskey C.C. Complete global stability for an SIR epidemic model with delay-Distributed or discrete. Nonlinear Anal. Real World Appl. 2010, 11:55-59.
    • (2010) Nonlinear Anal. Real World Appl. , vol.11 , pp. 55-59
    • McCluskey, C.C.1
  • 15
    • 0347758641 scopus 로고    scopus 로고
    • Analysis of an epidemic model with bistable equilibria using the Poincaré index
    • Moghadas S.M. Analysis of an epidemic model with bistable equilibria using the Poincaré index. Appl. Math. Comput. 2004, 149:689-702.
    • (2004) Appl. Math. Comput. , vol.149 , pp. 689-702
    • Moghadas, S.M.1
  • 16
    • 33750094360 scopus 로고    scopus 로고
    • Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate
    • Moghadas S.M., Alexander M.E. Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate. Math. Med. Biol. 2006, 23:231-254.
    • (2006) Math. Med. Biol. , vol.23 , pp. 231-254
    • Moghadas, S.M.1    Alexander, M.E.2
  • 17
    • 62549090964 scopus 로고    scopus 로고
    • A note on heroin epidemics
    • Mulone G., Straughan B. A note on heroin epidemics. Math. Biosci. 2009, 218:138-141.
    • (2009) Math. Biosci. , vol.218 , pp. 138-141
    • Mulone, G.1    Straughan, B.2
  • 18
    • 84875114855 scopus 로고    scopus 로고
    • Global stability for a class of a multi-group SIR epidemic model with varying population sizes
    • Muroya Y., Enatsu Y., Kuniya T. Global stability for a class of a multi-group SIR epidemic model with varying population sizes. Acta Math. Sci. 2013, 33:341-361.
    • (2013) Acta Math. Sci. , vol.33 , pp. 341-361
    • Muroya, Y.1    Enatsu, Y.2    Kuniya, T.3
  • 19
    • 84902511311 scopus 로고    scopus 로고
    • Global stability of a delayed SIRS computer virus propagation model
    • Muroya Y., Enatsu Y., Li H. Global stability of a delayed SIRS computer virus propagation model. Inter. J. Comput. Math. 2013, doi:10.1080/00207160.2013.790534.
    • (2013) Inter. J. Comput. Math.
    • Muroya, Y.1    Enatsu, Y.2    Li, H.3
  • 20
    • 79955524982 scopus 로고    scopus 로고
    • Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays
    • Muroya Y., Enatsu Y., Nakata Y. Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays. Nonlinear Anal. Real World Appl. 2011, 12:1897-1910.
    • (2011) Nonlinear Anal. Real World Appl. , vol.12 , pp. 1897-1910
    • Muroya, Y.1    Enatsu, Y.2    Nakata, Y.3
  • 21
    • 84859102947 scopus 로고    scopus 로고
    • On the global stability of SIRS epidemic models with distributed delays
    • Nakata Y., Enatsu Y., Muroya Y. On the global stability of SIRS epidemic models with distributed delays. Discrete Contin. Dyn. Syst. 2011, Supplement:1119-1128.
    • (2011) Discrete Contin. Dyn. Syst. , vol.Supplement , pp. 1119-1128
    • Nakata, Y.1    Enatsu, Y.2    Muroya, Y.3
  • 23
    • 34250220629 scopus 로고    scopus 로고
    • A delayed SIRS epidemic model with pulse vaccination
    • Pang G., Chen L. A delayed SIRS epidemic model with pulse vaccination. Chaos Solitons Fractals 2007, 34:1629-1635.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1629-1635
    • Pang, G.1    Chen, L.2
  • 24
    • 69049115668 scopus 로고    scopus 로고
    • Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear incidence rate
    • Tang Y., Huang D., Ruan S., Zhang W. Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear incidence rate. SIAM J. Appl. Math. 2008, 69:621-639.
    • (2008) SIAM J. Appl. Math. , vol.69 , pp. 621-639
    • Tang, Y.1    Huang, D.2    Ruan, S.3    Zhang, W.4
  • 25
    • 31244431921 scopus 로고    scopus 로고
    • Global behavior of an SEIRS epidemic model with time delays
    • Wang W. Global behavior of an SEIRS epidemic model with time delays. Appl. Math. Lett. 2002, 15:423-428.
    • (2002) Appl. Math. Lett. , vol.15 , pp. 423-428
    • Wang, W.1
  • 26
    • 84876676101 scopus 로고    scopus 로고
    • Dynamics of a heroin epidemic model with very population
    • Wang X., Yang J., Li X. Dynamics of a heroin epidemic model with very population. Appl. Math. 2011, 2:732-738.
    • (2011) Appl. Math. , vol.2 , pp. 732-738
    • Wang, X.1    Yang, J.2    Li, X.3
  • 27
    • 34249300962 scopus 로고    scopus 로고
    • Heroin epidemics, treatment and ODE modeling
    • White E., Comiskey C. Heroin epidemics, treatment and ODE modeling. Math. Biosci. 2007, 208:312-324.
    • (2007) Math. Biosci. , vol.208 , pp. 312-324
    • White, E.1    Comiskey, C.2
  • 28
    • 0032558714 scopus 로고    scopus 로고
    • Microparasite population dynamics and continuous immunity
    • White L.J., Medley G.F. Microparasite population dynamics and continuous immunity. Proc. R. Soc. Lond. Ser. B 1998, 265:1977-1983.
    • (1998) Proc. R. Soc. Lond. Ser. B , vol.265 , pp. 1977-1983
    • White, L.J.1    Medley, G.F.2
  • 29
    • 34547134261 scopus 로고    scopus 로고
    • Global analysis of an epidemic model with nonmonotone incidence rate
    • Xiao D., Ruan S. Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci. 2007, 208:419-429.
    • (2007) Math. Biosci. , vol.208 , pp. 419-429
    • Xiao, D.1    Ruan, S.2
  • 30
    • 67649304819 scopus 로고    scopus 로고
    • Stability of a delayed SIRS epidemic model with a nonlinear incidence rate
    • Xu R., Ma Z. Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. Chaos Solitons Fractals 2009, 41:2319-2325.
    • (2009) Chaos Solitons Fractals , vol.41 , pp. 2319-2325
    • Xu, R.1    Ma, Z.2
  • 31
    • 76549112764 scopus 로고    scopus 로고
    • Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models
    • Yang Y., Xiao D. Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models. Discrete Contin. Dyn. Syst. Ser. B 2010, 13:195-211.
    • (2010) Discrete Contin. Dyn. Syst. Ser. B , vol.13 , pp. 195-211
    • Yang, Y.1    Xiao, D.2
  • 32
    • 43649100484 scopus 로고    scopus 로고
    • Global behavior and permanence of SIRS epidemic model with time delay
    • Zhang T., Teng Z. Global behavior and permanence of SIRS epidemic model with time delay. Nonlinear Anal. Real World Appl. 2008, 9:1409-1424.
    • (2008) Nonlinear Anal. Real World Appl. , vol.9 , pp. 1409-1424
    • Zhang, T.1    Teng, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.