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Volumn 50, Issue 9-10, 2009, Pages 1498-1513

Analysis and control of an SEIR epidemic system with nonlinear transmission rate

Author keywords

Control; Differential and algebraic systems; Hyperchaos; SEIR epidemic model

Indexed keywords

BIFURCATION DIAGRAM; DIFFERENTIAL AND ALGEBRAIC EQUATIONS; DIFFERENTIAL AND ALGEBRAIC SYSTEMS; DYNAMICAL BEHAVIORS; EPIDEMIC SYSTEM; HYPERCHAOS; HYPERCHAOTIC; LYAPUNOV; LYAPUNOV EXPONENT SPECTRUM; NONLINEAR TRANSMISSION; NUMERICAL SIMULATION; POINCARE SECTIONS; SEASONAL FORCING; SEASONALITY; SEIR EPIDEMIC MODEL; STABILITY AND BIFURCATION; TRACKING CONTROLLER; TRANSMISSION RATES; VARYING PARAMETERS;

EID: 70349443386     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.07.014     Document Type: Article
Times cited : (92)

References (40)
  • 1
    • 0035050183 scopus 로고    scopus 로고
    • Global stability of an SEIS epidemic model with recruitment and a varying total population size
    • Fan M., Michael Y.L., and Wang K. Global stability of an SEIS epidemic model with recruitment and a varying total population size. Mathematical Biosciences 170 (2001) 199-208
    • (2001) Mathematical Biosciences , vol.170 , pp. 199-208
    • Fan, M.1    Michael, Y.L.2    Wang, K.3
  • 3
    • 0035452052 scopus 로고    scopus 로고
    • Threshold and stability results for an age-structured SEIR epidemic model
    • Li X.Z., Gupur G., and Zhu G.T. Threshold and stability results for an age-structured SEIR epidemic model. Computers & Mathematics with Applications 42 (2001) 883-907
    • (2001) Computers & Mathematics with Applications , vol.42 , pp. 883-907
    • Li, X.Z.1    Gupur, G.2    Zhu, G.T.3
  • 4
    • 0000336301 scopus 로고
    • Bifurcation and dynamic complexity in simple ecological models
    • May R.M., and Oster G.F. Bifurcation and dynamic complexity in simple ecological models. American Naturalist 110 (1976) 573-599
    • (1976) American Naturalist , vol.110 , pp. 573-599
    • May, R.M.1    Oster, G.F.2
  • 5
    • 18544380939 scopus 로고    scopus 로고
    • Complexity of an SIRS epidemic dynamics model with impulsive vaccination control
    • Zeng G.Z., Chen L.S., and Sun L.H. Complexity of an SIRS epidemic dynamics model with impulsive vaccination control. Chaos Solitons & Fractals 26 (2005) 495-505
    • (2005) Chaos Solitons & Fractals , vol.26 , pp. 495-505
    • Zeng, G.Z.1    Chen, L.S.2    Sun, L.H.3
  • 6
  • 7
    • 2542426854 scopus 로고    scopus 로고
    • SIS epidemics with household structure: the self-consistent field method
    • Ghoshal G., Sander L.M., and Sokolov I.M. SIS epidemics with household structure: the self-consistent field method. Mathematical Biosciences 190 (2004) 71-85
    • (2004) Mathematical Biosciences , vol.190 , pp. 71-85
    • Ghoshal, G.1    Sander, L.M.2    Sokolov, I.M.3
  • 10
    • 0031066070 scopus 로고    scopus 로고
    • Melnikov analysis of chaos in a simple epidemiological model
    • Glendinning P., and Perry L.P. Melnikov analysis of chaos in a simple epidemiological model. Journal of Mathematical Biology 35 (1997) 359-373
    • (1997) Journal of Mathematical Biology , vol.35 , pp. 359-373
    • Glendinning, P.1    Perry, L.P.2
  • 11
    • 0032812296 scopus 로고    scopus 로고
    • Global dynamics of an SEIR model with varying total population size
    • Michael Y.L., Graef J.R., Wang L.C., and Karsai J. Global dynamics of an SEIR model with varying total population size. Mathematical Biosciences 160 (1999) 191-213
    • (1999) Mathematical Biosciences , vol.160 , pp. 191-213
    • Michael, Y.L.1    Graef, J.R.2    Wang, L.C.3    Karsai, J.4
  • 12
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Kuznetsov Y.A., and Piccardi C. Bifurcation analysis of periodic SEIR and SIR epidemic models. Mathematical Biosciences 32 (1994) 109-121
    • (1994) Mathematical Biosciences , vol.32 , pp. 109-121
    • Kuznetsov, Y.A.1    Piccardi, C.2
  • 13
    • 0025196595 scopus 로고
    • Chaos versus periodicity: alternative hypotheses for childhood epidemics
    • Olsen L.F., and Schaffer W.M. Chaos versus periodicity: alternative hypotheses for childhood epidemics. Science 249 (1990) 499-504
    • (1990) Science , vol.249 , pp. 499-504
    • Olsen, L.F.1    Schaffer, W.M.2
  • 14
    • 33846820429 scopus 로고    scopus 로고
    • Global stability for an special SEIR epidemic model with nonlinear incidence rates
    • Sun C.J., Lin Y.P., and Tang S.P. Global stability for an special SEIR epidemic model with nonlinear incidence rates. Chaos Solitons & Fractals 33 (2007) 290-297
    • (2007) Chaos Solitons & Fractals , vol.33 , pp. 290-297
    • Sun, C.J.1    Lin, Y.P.2    Tang, S.P.3
  • 16
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • Liu W.M., Hethcote H.W., and Levin S.A. Dynamical behavior of epidemiological models with nonlinear incidence rates. Journal of Mathematical Biology 25 (1987) 359-380
    • (1987) Journal of Mathematical Biology , vol.25 , pp. 359-380
    • Liu, W.M.1    Hethcote, H.W.2    Levin, S.A.3
  • 17
    • 0030976773 scopus 로고    scopus 로고
    • Hopf bifurcation in epidemic models with a latent period and non-permanent immunity
    • Greenhalgh D. Hopf bifurcation in epidemic models with a latent period and non-permanent immunity. Mathematical and Computer Modelling 25 (1997) 85-107
    • (1997) Mathematical and Computer Modelling , vol.25 , pp. 85-107
    • Greenhalgh, D.1
  • 22
    • 0003459004 scopus 로고    scopus 로고
    • Springer-Verlag, Heidelberg New York
    • Dai L. Singular Control Systems (1998), Springer-Verlag, Heidelberg New York
    • (1998) Singular Control Systems
    • Dai, L.1
  • 24
    • 0037093075 scopus 로고    scopus 로고
    • The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model
    • Kamo M., and Sasaki A. The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model. Physica D 165 (2002) 228-241
    • (2002) Physica D , vol.165 , pp. 228-241
    • Kamo, M.1    Sasaki, A.2
  • 27
    • 34249306568 scopus 로고    scopus 로고
    • Chaotic control based on descriptor bioeconomic systems
    • Zhang Y., and Zhang Q.L. Chaotic control based on descriptor bioeconomic systems. Control and Decision 22 (2007) 445-452
    • (2007) Control and Decision , vol.22 , pp. 445-452
    • Zhang, Y.1    Zhang, Q.L.2
  • 28
    • 0036885488 scopus 로고    scopus 로고
    • Sliding mode control of hyperchaos in Rossler systems
    • Jyi M., Chen C.L., and Chen C.K. Sliding mode control of hyperchaos in Rossler systems. Chaos Solitons & Fractals 14 (2002) 1465-1476
    • (2002) Chaos Solitons & Fractals , vol.14 , pp. 1465-1476
    • Jyi, M.1    Chen, C.L.2    Chen, C.K.3
  • 29
    • 34248386538 scopus 로고    scopus 로고
    • Hyperchaos generated from the Lorenz chaotic system and its control
    • Jia Q. Hyperchaos generated from the Lorenz chaotic system and its control. Physics Letters A 366 (2007) 217-222
    • (2007) Physics Letters A , vol.366 , pp. 217-222
    • Jia, Q.1
  • 30
    • 34548586902 scopus 로고    scopus 로고
    • Hyperchaos synchronization and control on a new hyperchaotic attractor
    • Yan Z.Y., and Yu D. Hyperchaos synchronization and control on a new hyperchaotic attractor. Chaos Solitons & Fractals 35 (2008) 333-345
    • (2008) Chaos Solitons & Fractals , vol.35 , pp. 333-345
    • Yan, Z.Y.1    Yu, D.2
  • 31
    • 33947275245 scopus 로고    scopus 로고
    • Robust controlling hyperchaos of the Rossler system subject to input nonlinearities by using sliding mode control
    • Yau H.T., and Yan J.J. Robust controlling hyperchaos of the Rossler system subject to input nonlinearities by using sliding mode control. Chaos Solitons & Fractals 33 (2007) 1767-1776
    • (2007) Chaos Solitons & Fractals , vol.33 , pp. 1767-1776
    • Yau, H.T.1    Yan, J.J.2
  • 32
    • 0036885488 scopus 로고    scopus 로고
    • Sliding mode control of hyperchaos in Rossler systems
    • Jang M.J., Chen C.L., and Chen C.K. Sliding mode control of hyperchaos in Rossler systems. Chaos, Solitons & Fractals 14 (2002) 1465-1476
    • (2002) Chaos, Solitons & Fractals , vol.14 , pp. 1465-1476
    • Jang, M.J.1    Chen, C.L.2    Chen, C.K.3
  • 33
    • 38049079764 scopus 로고    scopus 로고
    • On control and synchronization in chaotic and hyperchaotic systems via linear feedback control
    • Rafikov M., and Balthazar J.M. On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Communications in Nonlinear Science and Numerical Simulation 13 (2008) 1246-1255
    • (2008) Communications in Nonlinear Science and Numerical Simulation , vol.13 , pp. 1246-1255
    • Rafikov, M.1    Balthazar, J.M.2
  • 34
    • 50249131353 scopus 로고    scopus 로고
    • Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters
    • Zhou X.B., Wu Y., Li Y., and Xue H.Q. Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters. Applied Mathematics and Computation 203 (2008) 80-85
    • (2008) Applied Mathematics and Computation , vol.203 , pp. 80-85
    • Zhou, X.B.1    Wu, Y.2    Li, Y.3    Xue, H.Q.4
  • 35
    • 18544387140 scopus 로고    scopus 로고
    • Controlling and tracking hyperchaotic Rossler system via active backstepping design
    • Zhang H., Ma X.K., Li M., and Zou J.L. Controlling and tracking hyperchaotic Rossler system via active backstepping design. Chaos, Solitons & Fractals 26 (2005) 353-361
    • (2005) Chaos, Solitons & Fractals , vol.26 , pp. 353-361
    • Zhang, H.1    Ma, X.K.2    Li, M.3    Zou, J.L.4
  • 36
    • 0035435432 scopus 로고    scopus 로고
    • Nonlinear control of differential algebraic model in power systems
    • Wang J., and Chen C. Nonlinear control of differential algebraic model in power systems. Proceedings of the CSEE 21 (2001) 15-18
    • (2001) Proceedings of the CSEE , vol.21 , pp. 15-18
    • Wang, J.1    Chen, C.2
  • 37
    • 45049085469 scopus 로고    scopus 로고
    • Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance 'bubble'
    • Broer H., Simo C., and Vitolo R. Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance 'bubble'. Physica D 237 (2008) 1773-1799
    • (2008) Physica D , vol.237 , pp. 1773-1799
    • Broer, H.1    Simo, C.2    Vitolo, R.3
  • 38
    • 56349155062 scopus 로고    scopus 로고
    • The Hopf-Saddle-Node bifurcation for fixed points of 3D- diffeomorphisms: The Arnol'd resonance web
    • Broer H., Simo C., and Vitolo R. The Hopf-Saddle-Node bifurcation for fixed points of 3D- diffeomorphisms: The Arnol'd resonance web. The Bulletin of The Belgian Mathematical Society-Simon Stevin 15 (2008) 769-787
    • (2008) The Bulletin of The Belgian Mathematical Society-Simon Stevin , vol.15 , pp. 769-787
    • Broer, H.1    Simo, C.2    Vitolo, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.