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Volumn 6, Issue 3, 2009, Pages 469-492

Optimal control applied to vaccination and treatment strategies for various epidemiological models

Author keywords

Epidemic; Optimal control; SEIR; SIR; SIRS; Vaccination

Indexed keywords

ANTIINFECTIVE AGENT;

EID: 70349647743     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.469     Document Type: Article
Times cited : (205)

References (33)
  • 1
    • 0001896288 scopus 로고
    • Population ecology of infectious disease agents
    • ed. R. M. May, Blackwell
    • R. M. Anderson, Population ecology of infectious disease agents, "Theoretical Ecology, Principles, and Applications" (ed. R. M. May), Blackwell, (1981), 318-355.
    • (1981) Theoretical Ecology, Principles, and Applications , pp. 318-355
    • Anderson, R.M.1
  • 2
    • 0034313015 scopus 로고    scopus 로고
    • Optimal control of deterministic epidemics
    • Horst Behncke, Optimal control of deterministic epidemics, Optimal Control Applied Methods, 21 (2000), 269-285.
    • (2000) Optimal Control Applied Methods , vol.21 , pp. 269-285
    • Behncke, H.1
  • 3
    • 4544238031 scopus 로고    scopus 로고
    • An attempt at a new analysis of the mortality caused by smallpox and the advantages of inoculation to prevent it
    • D. Bernoulli and S. Blower, An attempt at a new analysis of the mortality caused by smallpox and the advantages of inoculation to prevent it, Reviews in Medical Virology,.14 (2004), 275-288.
    • (2004) Reviews in Medical Virology , vol.14 , pp. 275-288
    • Bernoulli, D.1    Blower, S.2
  • 5
    • 33846857259 scopus 로고    scopus 로고
    • Some simple epidemic models
    • Fred Brauer, Some simple epidemic models, Math. BioSci. Eng., 3 (2006), 1-15.
    • (2006) Math. BioSci. Eng. , vol.3 , pp. 1-15
    • Brauer, F.1
  • 10
    • 0003347615 scopus 로고
    • Deterministic and stochastic optimal control
    • Springer-Verlag
    • Wendell H. Fleming and Raymond W. Rishel, "Deterministic and Stochastic Optimal Control," Applications of Mathematics, No.1, Springer-Verlag, 1975.
    • (1975) Applications of Mathematics , vol.1
    • Fleming, W.H.1    Rishel, R.W.2
  • 11
    • 0000275657 scopus 로고
    • A numerical method for solving parabolic equations with opposite orientations
    • W. K. Hackbush, A numerical method for solving parabolic equations with opposite orientations, Computing, 20 (1978), 229-240.
    • (1978) Computing , vol.20 , pp. 229-240
    • Hackbush, W.K.1
  • 12
    • 0036846383 scopus 로고    scopus 로고
    • Effect of quarantine in six endemic models for infectious diseases
    • Herbert Hethcote, Ma Zhien and Liao Shengbing, Effect of quarantine in six endemic models for infectious diseases, Mathematical Biosciences, 180 (2002), 141-160.
    • (2002) Mathematical Biosciences , vol.180 , pp. 141-160
    • Hethcote, H.1    Zhien, M.2    Shengbing, L.3
  • 13
    • 0000751578 scopus 로고
    • A Thousand and One Epidemic Models
    • ed. S. A. Levin, Springer-Verlag
    • H. W. Hethcote, A thousand and one epidemic models, "Frontiers in Theoretical Biology" (ed. S. A. Levin), Springer-Verlag, (1994) 504-515.
    • (1994) Frontiers in Theoretical Biology , pp. 504-515
    • Hethcote, H.W.1
  • 15
    • 0023887538 scopus 로고
    • Optimal ages of vaccination for measles
    • Herbert W. Hethcote, Optimal ages of vaccination for measles, Mathematical Biosciences, 89 (1988), 29-52.
    • (1988) Mathematical Biosciences , vol.89 , pp. 29-52
    • Hethcote, H.W.1
  • 16
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
    • (2000) SIAM Review , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 18
    • 0036631015 scopus 로고    scopus 로고
    • Optimal control of an HIV immunology model
    • Hem Raj Joshi, Optimal control of an HIV immunology model, Optimal Control Applications& Methods, 23 (2002), 199-213.
    • (2002) Optimal Control Applications & Methods , vol.23 , pp. 199-213
    • Joshi, H.R.1
  • 19
    • 0042762770 scopus 로고    scopus 로고
    • Optimal control of treatments in a two-strain tuberculosis
    • Series B
    • E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis,.Discrete and Continuous Dynamical Systems. Series B, 2 (2002), 473-482.
    • (2002) Discrete and Continuous Dynamical Systems , vol.2 , pp. 473-482
    • Jung, E.1    Lenhart, S.2    Feng, Z.3
  • 22
    • 0036055820 scopus 로고    scopus 로고
    • On optimal controls for a general mathematical model for chemotherapy of HIV
    • Anchorage, Alaska
    • Urszula Ledzewicz and Heinz Schaettler, On optimal controls for a general mathematical model for chemotherapy of HIV, Proceedings of the 2002 American Control Conference, Anchorage, Alaska, (2002), 3454-3459.
    • Proceedings of the 2002 American Control Conference , vol.2002 , pp. 3454-3459
    • Ledzewicz, U.1    Schaettler, H.2
  • 25
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • Wei Min Liu, Herbert W. Hethcote and Simon A. Levin, 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
  • 26
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • Wei Min Liu, Simon A. Levin and Yoh Iwasa Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, Journal of Mathematical Biology, 23 (1986), 187-204.
    • (1986) Journal of Mathematical Biology , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 27
    • 70349638193 scopus 로고    scopus 로고
    • Human population dynamics revisited with the logistic model: How much can be modeled and predicted?
    • C. Marchetti, P. S. Meyer and J. H. Ausubel, Human population dynamics revisited with the logistic model: How much can be modeled and predicted? Human Evolution, 19 (2004), 247-285.
    • (2004) Human Evolution , vol.19 , pp. 247-285
    • Marchetti, C.1    Meyer, P.S.2    Ausubel, J.H.3
  • 30
    • 0016338420 scopus 로고
    • Quantitative Guidelines for communicable disease control program: A complete synthesis
    • S. P. Sethi, Quantitative Guidelines for communicable disease control program: A complete synthesis, Biometrics, 30 (1974), 681-691.
    • (1974) Biometrics , vol.30 , pp. 681-691
    • Sethi, S.P.1
  • 31
    • 0034445348 scopus 로고    scopus 로고
    • Optimal control theory applied to the anti-viral treatment of AIDS, Decision and Control, 2000
    • IEEE
    • Felippe de Souza, M. A. L. Caetano and Takashi Yonoyama, Optimal control theory applied to the anti-viral treatment of AIDS, Decision and Control, 2000, Proceedings of the 39th IEEE Conference V. 5, IEEE, (2000), 4839-4844.
    • (2000) Proceedings of the 39th IEEE Conference , vol.5 , pp. 4839-4844
    • De Souza, F.1    Caetano, M.A.L.2    Yonoyama, T.3
  • 33
    • 1542298927 scopus 로고    scopus 로고
    • Simulating the SARS outbreak in Beijing with limited data
    • Wendi Wang and Shigui Ruan, Simulating the SARS outbreak in Beijing with limited data,.Journal of Theoretical Biology, 227 (2004), 369-379.
    • (2004) Journal of Theoretical Biology , vol.227 , pp. 369-379
    • Wang, W.1    Ruan, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.