메뉴 건너뛰기




Volumn 4, Issue 4, 2011, Pages 473-491

Mixed vaccination strategy in sirs epidemic model with seasonal variability on infection

Author keywords

basic reproduction number; Mixed vaccination strategy; seasonal variability

Indexed keywords


EID: 84857584076     PISSN: 17935245     EISSN: 17937159     Source Type: Journal    
DOI: 10.1142/S1793524511001337     Document Type: Article
Times cited : (18)

References (43)
  • 2
    • 33244460571 scopus 로고    scopus 로고
    • Mucormycosis in the Eastern Mediterranean: A seasonal disease
    • DOI 10.1017/S0950268805004930, PII S0950268805004930
    • M. R. Al-Ajam, A. R. Bizri, J. Mokhbat et al., Mucormycosis in the Eastern Mediterranean: A seasonal disease, Epidemiol. Infect. 134 (2006) 341-346. (Pubitemid 43280244)
    • (2006) Epidemiology and Infection , vol.134 , Issue.2 , pp. 341-346
    • Al-Ajam, M.R.1    Bizri, A.R.2    Mokhbat, J.3    Weedon, J.4    Lutwick, L.5
  • 4
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, J. Theor. Biol. 110 (1984) 665-679. (Pubitemid 15185682)
    • (1984) Journal of Theoretical Biology , vol.110 , Issue.4 , pp. 665-679
    • Aron, J.L.1    Schwartz, I.B.2
  • 5
    • 0036286405 scopus 로고    scopus 로고
    • Dengue: Description and forecasting of epidemics
    • P. Barbazan, S. Yoksan and J. P. Gonzalez, Dengue: Description and forecasting of epidemics, Microbes. Infect. 4 (2002) 699-705.
    • (2002) Microbes. Infect. , vol.4 , pp. 699-705
    • Barbazan, P.1    Yoksan, S.2    Gonzalez, J.P.3
  • 6
    • 0018041874 scopus 로고
    • A generalization of the Kermack-McKendrick deterministic epidemic model
    • DOI 10.1016/0025-5564(78)90006-8
    • V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci. 42 (1978) 43-61. (Pubitemid 9117153)
    • (1978) Mathematical Biosciences , vol.42 , Issue.1-2 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 7
    • 25644446425 scopus 로고
    • Some equations modeling growth process and gonorrhea epidemics
    • K. L. Cooke and J. A. Yorke, Some equations modeling growth process and gonorrhea epidemics, Math. Biosci. 16 (1973) 75-107.
    • (1973) Math. Biosci. , vol.16 , pp. 75-107
    • Cooke, K.L.1    Yorke, J.A.2
  • 8
    • 11144311134 scopus 로고    scopus 로고
    • Exploring 30 years of malaria case data in KwaZulu-Natal, South Africa: Part I. The impact of climatic factors
    • DOI 10.1111/j.1365-3156.2004.01340.x
    • M. H. Craig, I. Kleinschmidt, J. B. Nawn et al., Exploring 30 years of malaria case data in KwaZulu-Natal, South Africa: Part I. The impact of climatic factors, Trop. Med. Int. Health 9 (2004) 1247-1257. (Pubitemid 40037160)
    • (2004) Tropical Medicine and International Health , vol.9 , Issue.12 , pp. 1247-1257
    • Craig, M.H.1    Kleinschmidt, I.2    Nawn, J.B.3    Le Sueur, D.4    Sharp, B.L.5
  • 9
    • 0002091257 scopus 로고
    • How does transmission depend on population size?
    • ed. D. Mollison Cambridge University Press, Cambridge
    • M. C. M. de Jong, O. Diekmann and J. A. P. Heesterbeek, How does transmission depend on population size? in Human Infectious Diseases, Epidemic Models, ed. D. Mollison (Cambridge University Press, Cambridge, 1995), pp. 84-94.
    • (1995) Human Infectious Diseases, Epidemic Models , pp. 84-94
    • De Jong, M.C.M.1    Diekmann, O.2    Heesterbeek, J.A.P.3
  • 10
    • 0043263962 scopus 로고    scopus 로고
    • Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population
    • W. R. Derrick and P. van den Driessche, Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population, Discrete Contin. Dynam. Syst. Ser. B 3 (2003) 299-309. (Pubitemid 37073309)
    • (2003) Discrete and Continuous Dynamical Systems - Series B , vol.3 , Issue.2 , pp. 299-309
    • Derrick, W.R.1    Van Den Driessche, P.2
  • 11
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations, in
    • eds. J. Berger, W. Bühler, R. Repges and P. Tautu, Lecture Notes in Biomathematics Springer, Berlin
    • K. Dietz, The incidence of infectious diseases under the influence of seasonal fluctuations, in Proc. Workshop on Mathematical Modeling in Medicine, Mainz, eds. J. Berger, W. Bühler, R. Repges and P. Tautu, Lecture Notes in Biomathematics (Springer, Berlin, 1976), pp. 1-15.
    • (1976) Proc. Workshop on Mathematical Modeling in Medicine, Mainz , pp. 1-15
    • Dietz, K.1
  • 12
    • 0036291194 scopus 로고    scopus 로고
    • Stability properties of pulse vaccination strategy in SEIR epidemic model
    • DOI 10.1016/S0025-5564(02)00095-0, PII S0025556402000950
    • A. D'Onofrio, Stability properties of pulse vaccination strategy in SEIR epidemic model, Math. Biosci. 179 (2002) 57-72. (Pubitemid 34686427)
    • (2002) Mathematical Biosciences , vol.179 , Issue.1 , pp. 57-72
    • D'Onofrio, A.1
  • 13
    • 1242264916 scopus 로고    scopus 로고
    • Mixed pulse vaccination strategy in epidemic model with realistic distributed infectious and latent times
    • A. D'Onofrio, Mixed pulse vaccination strategy in epidemic model with realistic distributed infectious and latent times, Appl. Math. Comput. 151 (2004) 181-187.
    • (2004) Appl. Math. Comput. , vol.151 , pp. 181-187
    • D'Onofrio, A.1
  • 15
    • 0036643943 scopus 로고    scopus 로고
    • Ecology and evolution of the flu
    • DOI 10.1016/S0169-5347(02)02502-8, PII S0169534702025028
    • D. J. D. Earn, J. Dushoff and S. A. Levin, Ecology and evolution of the flu, Trends Ecol. Evol. 17 (2002) 334-340. (Pubitemid 34628660)
    • (2002) Trends in Ecology and Evolution , vol.17 , Issue.7 , pp. 334-340
    • Earn, D.J.D.1    Dushoff, J.2    Levin, S.A.3
  • 16
    • 0029014859 scopus 로고
    • Multi-annual outbreaks of childhood disease revisited: The impact of isolation
    • Z. Feng and R. H. Thieme, Multi-annual outbreaks of childhood disease revisited: The impact of isolation, Math. Biosci. 128 (1995) 93-130.
    • (1995) Math. Biosci. , vol.128 , pp. 93-130
    • Feng, Z.1    Thieme, R.H.2
  • 17
    • 33746833233 scopus 로고    scopus 로고
    • Analysis of a delayed epidemic model with pulse vaccination and saturation incidence
    • DOI 10.1016/j.vaccine.2006.05.018, PII S0264410X06005779
    • S. Gao, L Chen, J. J. Nieto et al., Analysis of a delayed epidemic model with pulse vaccination and saturation incidence, Vaccine 24 (2006) 6037-6045. (Pubitemid 44175617)
    • (2006) Vaccine , vol.24 , Issue.35-36 , pp. 6037-6045
    • Gao, S.1    Chen, L.2    Nieto, J.J.3    Torres, A.4
  • 18
    • 58049141205 scopus 로고    scopus 로고
    • Analysis of an SEIRS epidemic model with time delays and pulse vaccination
    • S. Gao, L. Chen and Z. Teng, Analysis of an SEIRS epidemic model with time delays and pulse vaccination, Rocky Mountain J. Math. 38 (2008) 1385-1402.
    • (2008) Rocky Mountain J. Math. , vol.38 , pp. 1385-1402
    • Gao, S.1    Chen, L.2    Teng, Z.3
  • 19
    • 5444262735 scopus 로고    scopus 로고
    • Hopf bifurcation in two SIRS density dependent epidemic models
    • DOI 10.1016/j.mcm.2004.06.007, PII S0895717704800979
    • D. Greenhalgh, Q. J. A. Khan and F. I. Lewis, Hopf bifurcation in two SIRS density dependent epidemic models, Math. Comput. Modelling 39 (2004) 1261-1283. (Pubitemid 39350867)
    • (2004) Mathematical and Computer Modelling , vol.39 , Issue.11-12 , pp. 1261-1283
    • Greenhalgh, D.1    Khan, Q.J.A.2    Lewis, F.I.3
  • 20
    • 0017228276 scopus 로고
    • Qualitative analysis for communicable disease models
    • H.W. Hethcote, Qualitative analysis for communicable disease models, Math. Biosci. 28 (1976) 335-356.
    • (1976) Math. Biosci. , vol.28 , pp. 335-356
    • Hethcote, H.W.1
  • 21
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious disease
    • H. W. Hethcote, The mathematics of infectious disease, SIAM Rev. 42 (2000) 599-653.
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 22
    • 69249209635 scopus 로고    scopus 로고
    • Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination
    • G. Jiang and Q. Yang, Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination, Appl. Math. Comput. 215 (2009) 1035-1046.
    • (2009) Appl. Math. Comput. , vol.215 , pp. 1035-1046
    • Jiang, G.1    Yang, Q.2
  • 23
    • 84863116392 scopus 로고    scopus 로고
    • Pulse vaccination in the periodic infection rate SIR epidemic model
    • Z. Jin, M. Haque and Q. Liu, Pulse vaccination in the periodic infection rate SIR epidemic model, Int. J. Biomath. 1 (2008) 409-432.
    • (2008) Int. J. Biomath. , vol.1 , pp. 409-432
    • Jin, Z.1    Haque, M.2    Liu, Q.3
  • 24
    • 0000998185 scopus 로고
    • A contributions to the mathematical theory of epidemics I
    • W. O. Kermack and A. G. McKendrick, A contributions to the mathematical theory of epidemics I, Proc. R. Soc. Lond. A 115 (1927) 700-721.
    • (1927) Proc. R. Soc. Lond. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 25
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • DOI 10.1016/S0025-5564(00)00003-1, PII S0025556400000031
    • C. Kribs-Zaleta and J. X. Velasco-Hernández, A simple vaccination model with multiple endemic states, Math. Biosci. 164 (2000) 183-201. (Pubitemid 30211016)
    • (2000) Mathematical Biosciences , vol.164 , Issue.2 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernandez, J.X.2
  • 26
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • DOI 10.1007/BF00276956
    • W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol. 23 (1986) 187-204. (Pubitemid 16153721)
    • (1985) Journal of Mathematical Biology , vol.23 , Issue.2 , pp. 187-204
    • Liu, W.-M.1    Levin, S.A.2    Iwasa, Y.3
  • 27
    • 44849133934 scopus 로고    scopus 로고
    • SVIR epidemic models with vaccination strategies
    • DOI 10.1016/j.jtbi.2007.10.014, PII S0022519307005115
    • X. Liu, Y. Takeuchi and S. Iwami, SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 (2008) 1-11. (Pubitemid 351794279)
    • (2008) Journal of Theoretical Biology , vol.253 , Issue.1 , pp. 1-11
    • Liu, X.1    Takeuchi, Y.2    Iwami, S.3
  • 28
    • 0015739604 scopus 로고
    • Recurrent outbreaks of measles, chickenpox and mumps: I. Seasonal variation in contact rates
    • W. London and J. A. Yorke, Recurrent outbreaks of measles, chickenpox and mumps: I. seasonal variation in contact rates, Amer. J. Epidemiol. 98 (1973) 453-468.
    • (1973) Amer. J. Epidemiol. , vol.98 , pp. 453-468
    • London, W.1    Yorke, J.A.2
  • 29
    • 0037195889 scopus 로고    scopus 로고
    • The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission
    • PII S0895717702002571
    • Z. Lu, X. Chi and L. Chen, The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission, Math. Comput. Modelling 36 (2002) 1039-1057. (Pubitemid 35456633)
    • (2002) Mathematical and Computer Modelling , vol.36 , Issue.9-10 , pp. 1039-1057
    • Lu, Z.1    Chi, X.2    Chen, L.3
  • 30
    • 77949274591 scopus 로고    scopus 로고
    • Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects
    • X. Meng, Z. Li and X. Wang, Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects, Nonlinear Dynam. 59 (2010) 503-513.
    • (2010) Nonlinear Dynam. , vol.59 , pp. 503-513
    • Meng, X.1    Li, Z.2    Wang, X.3
  • 31
    • 34548404314 scopus 로고    scopus 로고
    • The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study
    • DOI 10.1016/j.compbiomed.2007.02.007, PII S0010482507000376
    • I. A. Moneim, The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study, Comput. Biol. Med. 37 (2007) 1582-1590. (Pubitemid 47362101)
    • (2007) Computers in Biology and Medicine , vol.37 , Issue.11 , pp. 1582-1590
    • Moneim, I.A.1
  • 33
    • 84863115736 scopus 로고    scopus 로고
    • Two different vaccination strategies in an SIR epidemic model with saturated infectious force
    • Y. Pei, S. Liu, L. Chen et al., Two different vaccination strategies in an SIR epidemic model with saturated infectious force, Int. J. Biomath. 1 (2008) 147-160.
    • (2008) Int. J. Biomath. , vol.1 , pp. 147-160
    • Pei, Y.1    Liu, S.2    Chen, L.3
  • 34
    • 0037429355 scopus 로고    scopus 로고
    • Dynamical behavior of an epidemic model with a nonlinear incidence rate
    • DOI 10.1016/S0022-0396(02)00089-X, PII S002203960200089X
    • S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations 188 (2003) 135-163. (Pubitemid 36233149)
    • (2003) Journal of Differential Equations , vol.188 , Issue.1 , pp. 135-163
    • Ruan, S.1    Wang, W.2
  • 35
    • 0026451408 scopus 로고
    • Small amplitude, long period outbreaks in seasonally driven epidemics
    • I. B. Schwartz, Small amplitude, long period outbreaks in seasonally driven epidemics, J. Math. Biol. 30 (1992) 473-491.
    • (1992) J. Math. Biol. , vol.30 , pp. 473-491
    • Schwartz, I.B.1
  • 36
    • 0034143395 scopus 로고    scopus 로고
    • Theoretical examination of the pulse vaccination policy in the SIR epidemic model
    • DOI 10.1016/S0895-7177(00)00040-6, PII S0895717700000406
    • B. Shulgin, L. Stone and Z. Agur, Theoretical examinations of pulse vaccination policy in the SIR epidemic model, Math. Comput. Modelling 31 (2000) 207-215. (Pubitemid 30124398)
    • (2000) Mathematical and Computer Modelling , vol.31 , Issue.4-5 , pp. 207-215
    • Stone, L.1    Shulgin, B.2    Agur, Z.3
  • 37
    • 0034198679 scopus 로고    scopus 로고
    • A simple SIS epidemic model with a backward bifurcation
    • P. van den Driessche and J.Watmough, A simple SIS epidemic model with a backward bifurcation, J. Math. Biol. 40 (2000) 525-540.
    • (2000) J. Math. Biol. , vol.40 , pp. 525-540
    • Van Den Driessche, P.1    Watmough, J.2
  • 38
    • 77950917649 scopus 로고    scopus 로고
    • The dynamics of an epidemic model for pest control with impulsive effect
    • L.Wang, L. Chen and J. J. Nieto, The dynamics of an epidemic model for pest control with impulsive effect, Nonlinear Anal. Real World Appl. 11 (2010) 1374-1386.
    • (2010) Nonlinear Anal. Real World Appl. , vol.11 , pp. 1374-1386
    • Wang, L.1    Chen, L.2    Nieto, J.J.3
  • 41
    • 43649101953 scopus 로고    scopus 로고
    • A delayed epidemic model with stage-structure and pulses for pest management strategy
    • DOI 10.1016/j.nonrwa.2007.05.004, PII S1468121807000934
    • H. Zhang, L. Chen and J. J. Nieto, A delayed epidemic model with stage-structure and pulses for pest management strategy, Nonlinear Anal. Real World Appl. 9 (2008) 1714-1726. (Pubitemid 351685810)
    • (2008) Nonlinear Analysis: Real World Applications , vol.9 , Issue.4 , pp. 1714-1726
    • Zhang, H.1    Chen, L.2    Nieto, J.J.3
  • 42
    • 61549085953 scopus 로고    scopus 로고
    • Analysis of a delayed SIR model with nonlinear incidence rate
    • Article ID 636153
    • J. Zhang, Z. Jin, Q. Liu et al., Analysis of a delayed SIR model with nonlinear incidence rate, Discrete Dyn. Nat. Soc. 2008 (2008) Article ID 636153, 16 pp.
    • (2008) Discrete Dyn. Nat. Soc. 2008 , pp. 16
    • Zhang, J.1    Jin, Z.2    Liu, Q.3
  • 43
    • 56549115873 scopus 로고    scopus 로고
    • Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment
    • X. Zhang and X. N. Liu, Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment, Nonlinear Anal. Real World Appl. 10 (2009) 565-575.
    • (2009) Nonlinear Anal. Real World Appl. , vol.10 , pp. 565-575
    • Zhang, X.1    Liu, X.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.