메뉴 건너뛰기




Volumn 59, Issue 1, 2011, Pages 1-28

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

Author keywords

Influenza model; Optimal control; Sensitivity analysis; Treatment; Vaccination

Indexed keywords

ANTIVIRUS AGENT; INFLUENZA VACCINE;

EID: 79952184781     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10441-010-9095-8     Document Type: Article
Times cited : (90)

References (56)
  • 1
    • 77952856693 scopus 로고    scopus 로고
    • Optimal chemoprophylaxis and treatment control strategies of a tuberculosis transmission model
    • Agusto FB (2009a) Optimal chemoprophylaxis and treatment control strategies of a tuberculosis transmission model. World J Model Simul 5(3): 163-173.
    • (2009) World J Model Simul , vol.5 , Issue.3 , pp. 163-173
    • Agusto, F.B.1
  • 2
    • 84895356796 scopus 로고    scopus 로고
    • Application of optimal control to the epidemiology of HIV-malaria co-infection
    • J. M. Tchuenche and Z. Mukandavire (Eds.), New York: Nova Sciences Publishers, Inc
    • Agusto FB (2009b) Application of optimal control to the epidemiology of HIV-malaria co-infection. In: Tchuenche JM, Mukandavire Z (eds) Advances in disease epidemiology. Nova Sciences Publishers, Inc., New York, 139-167.
    • (2009) Advances in Disease Epidemiology , pp. 139-167
    • Agusto, F.B.1
  • 4
    • 38349131002 scopus 로고    scopus 로고
    • A delay differential model for pandemic influenza with antiviral treatment
    • Alexander ME, Moghadas SM, Röst G, Jianhong W (2007) A delay differential model for pandemic influenza with antiviral treatment. Bull Math Biol 70(2): 382-397.
    • (2007) Bull Math Biol , vol.70 , Issue.2 , pp. 382-397
    • Alexander, M.E.1    Moghadas, S.M.2    Röst, G.3    Jianhong, W.4
  • 6
    • 0041529714 scopus 로고    scopus 로고
    • Transients and attractors in epidemics
    • Bauch CT, Earn D (2003) Transients and attractors in epidemics. Proc Royal Soc Lond A 270: 1573-1578.
    • (2003) Proc Royal Soc Lond A , vol.270 , pp. 1573-1578
    • Bauch, C.T.1    Earn, D.2
  • 7
    • 67349168121 scopus 로고    scopus 로고
    • Scheduling of measles vaccination in low-income countries: projections of a dynamic model
    • Bauch CT, Szusz E, Garrison LP (2009) Scheduling of measles vaccination in low-income countries: projections of a dynamic model. Vaccine 27(31): 4090-4098.
    • (2009) Vaccine , vol.27 , Issue.31 , pp. 4090-4098
    • Bauch, C.T.1    Szusz, E.2    Garrison, L.P.3
  • 8
    • 67650908870 scopus 로고    scopus 로고
    • Optimal control of vector-borne diseases: treatment and prevention
    • Blayneh K, Cao Y, Kwon H-D (2009) Optimal control of vector-borne diseases: treatment and prevention. Discret Continuous Dyn Syst Series B 11(3): 587-611.
    • (2009) Discret Continuous Dyn Syst Series B , vol.11 , Issue.3 , pp. 587-611
    • Blayneh, K.1    Cao, Y.2    Kwon, H.-D.3
  • 9
    • 79952194101 scopus 로고    scopus 로고
    • Optimal vaccination strategies for an influenza-like illness in a heterogeneous population
    • Gumel AB, Castillo-Chavez C, Mickens RE, Clemence DP (eds), AMS Contemporary Mathematics Book Series 410
    • Bowman C, Gumel AB (2006) Optimal vaccination strategies for an influenza-like illness in a heterogeneous population. In: Gumel AB, Castillo-Chavez C, Mickens RE, Clemence DP (eds) Mathematical studies on human disease dynamics, emerging paradigms and challenges. AMS Contemporary Mathematics Book Series 410, pp 31-50.
    • (2006) Mathematical studies on human disease dynamics, emerging paradigms and challenges , pp. 31-50
    • Bowman, C.1    Gumel, A.B.2
  • 10
    • 10144259346 scopus 로고    scopus 로고
    • Backward bifurcations in simple vaccination models
    • Brauer F (2004) Backward bifurcations in simple vaccination models. J Math Anal Appl 298: 418-431.
    • (2004) J Math Anal Appl , vol.298 , pp. 418-431
    • Brauer, F.1
  • 11
    • 0034976407 scopus 로고    scopus 로고
    • Model for transmission of disease with immigration of infectives
    • Brauer F, van Den Driessche P (2001) Model for transmission of disease with immigration of infectives. Math Biosci 171: 143-154.
    • (2001) Math Biosci , vol.171 , pp. 143-154
    • Brauer, F.1    Vanden Driessche, P.2
  • 12
    • 0035265524 scopus 로고    scopus 로고
    • Optimal and sub-optimal control in Dengue epidemics
    • Caetano MAL, Yoneyama T (2001) Optimal and sub-optimal control in Dengue epidemics. Opt Contr Appl Meth 22: 63-73.
    • (2001) Opt Contr Appl Meth , vol.22 , pp. 63-73
    • Caetano, M.A.L.1    Yoneyama, T.2
  • 14
    • 47349102730 scopus 로고    scopus 로고
    • Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model
    • Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70: 1272-1296.
    • (2008) Bull Math Biol , vol.70 , pp. 1272-1296
    • Chitnis, N.1    Hyman, J.M.2    Cushing, J.M.3
  • 15
    • 33846188172 scopus 로고    scopus 로고
    • Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland
    • Chowell G, Ammon CE, Hengartner N, Mac Hyman JM (2006a) Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland. Vaccine 24: 6747-6750.
    • (2006) Vaccine , vol.24 , pp. 6747-6750
    • Chowell, G.1    Ammon, C.E.2    Hengartner, N.3    Mac Hyman, J.M.4
  • 16
    • 33745626761 scopus 로고    scopus 로고
    • Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions
    • Chowell G, Ammon CE, Hengartner N, Mac Hyman JM (2006b) Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions. J Theor Biol 241: 193-204.
    • (2006) J Theor Biol , vol.241 , pp. 193-204
    • Chowell, G.1    Ammon, C.E.2    Hengartner, N.3    Mac Hyman, J.M.4
  • 17
    • 33846862467 scopus 로고    scopus 로고
    • Comparative estimation of the reproduction number for pandemic influenza from daily case notification data
    • Chowell G, Nishiura H, Bettencourt LMA (2006c) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J R Soc Interface 4(12): 155-166.
    • (2006) J R Soc Interface , vol.4 , Issue.12 , pp. 155-166
    • Chowell, G.1    Nishiura, H.2    Bettencourt, L.M.A.3
  • 19
    • 0033539297 scopus 로고    scopus 로고
    • Influenza
    • Cox NJ, Subbarao K (1999) Influenza. Lancet 354: 1277-1282.
    • (1999) Lancet , vol.354 , pp. 1277-1282
    • Cox, N.J.1    Subbarao, K.2
  • 20
    • 21244476462 scopus 로고    scopus 로고
    • Optimal HIV treatment by maximising immune response
    • Culshaw RV (2004) Optimal HIV treatment by maximising immune response. J Math Biol 48: 545-562.
    • (2004) J Math Biol , vol.48 , pp. 545-562
    • Culshaw, R.V.1
  • 25
    • 34147148647 scopus 로고    scopus 로고
    • Avian-human influenza epidemic model
    • Iwami S, Takeuchi Y, Liu X (2006) Avian-human influenza epidemic model. Math Biosci 207: 1-25.
    • (2006) Math Biosci , vol.207 , pp. 1-25
    • Iwami, S.1    Takeuchi, Y.2    Liu, X.3
  • 26
    • 0036631015 scopus 로고    scopus 로고
    • Optimal control of an HIV immunology model
    • Joshi HR (2002) Optimal control of an HIV immunology model. Optim Control Appl Math 23: 199-213.
    • (2002) Optim Control Appl Math , vol.23 , pp. 199-213
    • Joshi, H.R.1
  • 27
    • 0042762770 scopus 로고    scopus 로고
    • Optimal control of treatments in a two-strain tuberculosis model
    • Jung E, Lenhart S, Feng Z (2002) Optimal control of treatments in a two-strain tuberculosis model. Discr Cont Dyn Syst B 2(4): 473-482.
    • (2002) Discr Cont Dyn Syst B , vol.2 , Issue.4 , pp. 473-482
    • Jung, E.1    Lenhart, S.2    Feng, Z.3
  • 28
    • 33744999665 scopus 로고    scopus 로고
    • Optimal control and infectiology: application to an HIV/AIDS model
    • Karrakchou J, Rachik M, Gourari S (2006) Optimal control and infectiology: application to an HIV/AIDS model. Appl Math Comput 177: 807-818.
    • (2006) Appl Math Comput , vol.177 , pp. 807-818
    • Karrakchou, J.1    Rachik, M.2    Gourari, S.3
  • 29
    • 78650375493 scopus 로고    scopus 로고
    • Optimal control applied to native-invasive population dynamics
    • Kern D, Lenhart S, Miller R, Yong J (2007) Optimal control applied to native-invasive population dynamics. J Biol Dyn 1(4): 413-426.
    • (2007) J Biol Dyn , vol.1 , Issue.4 , pp. 413-426
    • Kern, D.1    Lenhart, S.2    Miller, R.3    Yong, J.4
  • 30
    • 0031204179 scopus 로고    scopus 로고
    • Optimal control of the chemotherapy of HIV
    • Kirschner D, Lenhart S, Serbin S (1997) Optimal control of the chemotherapy of HIV. J Math Biol 35: 775-792.
    • (1997) J Math Biol , vol.35 , pp. 775-792
    • Kirschner, D.1    Lenhart, S.2    Serbin, S.3
  • 31
    • 34248225294 scopus 로고    scopus 로고
    • Optimal treatment strategies derived from a HIV model with drug-resistant mutants
    • Kwon H-D (2006) Optimal treatment strategies derived from a HIV model with drug-resistant mutants. Appl Math Comput 188(2): 1193-1204.
    • (2006) Appl Math Comput , vol.188 , Issue.2 , pp. 1193-1204
    • Kwon, H.-D.1
  • 33
    • 0001510210 scopus 로고
    • Application of distributed parameter control model in wildlife damage management
    • Lenhart S, Bhat MG (1992) Application of distributed parameter control model in wildlife damage management. Math Models Methods Appl Sci 2(4): 423-439.
    • (1992) Math Models Methods Appl Sci , vol.2 , Issue.4 , pp. 423-439
    • Lenhart, S.1    Bhat, M.G.2
  • 36
    • 0034959807 scopus 로고    scopus 로고
    • The impact of specific virus diagnosis and monitoring for antiviral treatment
    • Linde A (2001) The impact of specific virus diagnosis and monitoring for antiviral treatment. Antiviral Res 51: 81-94.
    • (2001) Antiviral Res , vol.51 , pp. 81-94
    • Linde, A.1
  • 38
    • 4944233809 scopus 로고    scopus 로고
    • Modelling the effect of imperfect vaccines on disease epidemiology
    • Moghadas SM (2004) Modelling the effect of imperfect vaccines on disease epidemiology. Discrete Cont Dyn Syst B 4(4): 999-1012.
    • (2004) Discrete Cont Dyn Syst B , vol.4 , Issue.4 , pp. 999-1012
    • Moghadas, S.M.1
  • 39
    • 33845641295 scopus 로고    scopus 로고
    • Estimation of potential global pandemic influenza mortality on the basis of vital registry data from the 1918-20 pandemic: a quantitative analysis
    • Murray CJ, Lopez AD, Chin B, Feehan D, Hill KH (2006) Estimation of potential global pandemic influenza mortality on the basis of vital registry data from the 1918-20 pandemic: a quantitative analysis. Lancet 368: 2211-2218.
    • (2006) Lancet , vol.368 , pp. 2211-2218
    • Murray, C.J.1    Lopez, A.D.2    Chin, B.3    Feehan, D.4    Hill, K.H.5
  • 40
    • 34250371355 scopus 로고    scopus 로고
    • Time variations in the transmissibility of pandemic influenza in Prussia, Germany
    • from 1918-19
    • Nishiura H (2007) Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918-19. Theor Biol Med Modell (Open Access) 1-9.
    • (2007) Theor Biol Med Modell (Open Access)
    • Nishiura, H.1
  • 41
    • 34249797897 scopus 로고    scopus 로고
    • Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands
    • Nunõ M, Chowell G, Gumel AB (2006a) Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands. J R Soc Interf 4(14): 505-521.
    • (2006) J R Soc Interf , vol.4 , Issue.14 , pp. 505-521
    • Nunõ, M.1    Chowell, G.2    Gumel, A.B.3
  • 42
    • 33750968462 scopus 로고    scopus 로고
    • On the role of cross-immunity and vaccines on the survival of less fit flu-strains
    • Nunõ M, Chowell G, Wang X, Castillo-Chavez C (2006b) On the role of cross-immunity and vaccines on the survival of less fit flu-strains. Theor Popul Biol 71(1): 20-29.
    • (2006) Theor Popul Biol , vol.71 , Issue.1 , pp. 20-29
    • Nunõ, M.1    Chowell, G.2    Wang, X.3    Castillo-Chavez, C.4
  • 43
    • 14744296414 scopus 로고    scopus 로고
    • Finding optimal vaccination strategies for pandemic influenza using genetic algorithms
    • Patel R, Longini IM Jr, Halloran ME (2005) Finding optimal vaccination strategies for pandemic influenza using genetic algorithms. J Theor Biol 234: 201-212.
    • (2005) J Theor Biol , vol.234 , pp. 201-212
    • Patel, R.1    Longini, J.I.M.2    Halloran, M.E.3
  • 44
    • 26844567211 scopus 로고    scopus 로고
    • The effect of vaccinations in an immigrant model
    • Piccolo C III, Billings L (2005) The effect of vaccinations in an immigrant model. Math Comp Mod 42: 291-299.
    • (2005) Math Comp Mod , vol.42 , pp. 291-299
    • Piccolo III, C.1    Billings, L.2
  • 45
    • 0003716451 scopus 로고
    • The mathematical theory of optimal control process
    • Gordon and Breach Science Publishers, New York
    • Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1986) The mathematical theory of optimal control process, vol 4. Gordon and Breach Science Publishers, New York.
    • (1986) , vol.4
    • Pontryagin, L.S.1    Boltyanskii, V.G.2    Gamkrelidze, R.V.3    Mishchenko, E.F.4
  • 46
    • 73649105468 scopus 로고    scopus 로고
    • Transmission dynamics of an influenza model with vaccination and antiviral treatment
    • Qiu Z, Feng Z (2009) Transmission dynamics of an influenza model with vaccination and antiviral treatment. Bull Math Biol 72(1): 1-33.
    • (2009) Bull Math Biol , vol.72 , Issue.1 , pp. 1-33
    • Qiu, Z.1    Feng, Z.2
  • 47
    • 0036831479 scopus 로고    scopus 로고
    • Influenza. Past, present and future
    • Regan SF, Fowler C (2002) Influenza. Past, present and future. J Gerontol Nurs 28: 30-37.
    • (2002) J Gerontol Nurs , vol.28 , pp. 30-37
    • Regan, S.F.1    Fowler, C.2
  • 48
    • 79952193470 scopus 로고    scopus 로고
    • A mathematical analysis of influenza with treatment and vaccination-chap. 2
    • In: Tchuenche JM, Chiyaka C (eds) Infectious disease modelling research progress
    • Rwezaura H, Mtisi E, Tchuenche JM (2009) A mathematical analysis of influenza with treatment and vaccination-chap. 2 In: Tchuenche JM, Chiyaka C (eds) Infectious disease modelling research progress. Nova Science Publishers Inc, pp 31-84.
    • (2009) Nova Science Publishers Inc , pp. 31-84
    • Rwezaura, H.1    Mtisi, E.2    Tchuenche, J.M.3
  • 49
    • 36148968419 scopus 로고    scopus 로고
    • Role of incidence function in vaccine-induced backward bifurcation in some HIV models
    • Sharomi O, Podder CN, Gumel AB, Elbasha EH, Watmough J (2007) Role of incidence function in vaccine-induced backward bifurcation in some HIV models. Math Biosci 210: 436-463.
    • (2007) Math Biosci , vol.210 , pp. 436-463
    • Sharomi, O.1    Podder, C.N.2    Gumel, A.B.3    Elbasha, E.H.4    Watmough, J.5
  • 50
    • 33846946117 scopus 로고    scopus 로고
    • A note on epidemic models with infective immigrants and vaccination
    • Shim E (2006) A note on epidemic models with infective immigrants and vaccination. Math Biosci Eng 3: 557-566.
    • (2006) Math Biosci Eng , vol.3 , pp. 557-566
    • Shim, E.1
  • 51
    • 79952190119 scopus 로고    scopus 로고
    • Influenza pandemic, efforts under way to address constraints on using antivirals and vaccines to forestall a pandemic
    • USGAO
    • USGAO (2007) Influenza pandemic, efforts under way to address constraints on using antivirals and vaccines to forestall a pandemic, Report to Congressional Requesters.
    • (2007) Report to Congressional Requesters
  • 52
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180: 29-48.
    • (2002) Math Biosci , vol.180 , pp. 29-48
    • Vanden Driessche, P.1    Watmough, J.2
  • 54
    • 30944449337 scopus 로고    scopus 로고
    • Non-pharmaceutical interventions for pandemic influenza, national and community measures
    • World Health Organization Writing Group
    • World Health Organization Writing Group (2006) Non-pharmaceutical interventions for pandemic influenza, national and community measures. Emerg Infect Dis 12: 88-94.
    • (2006) Emerg Infect Dis , vol.12 , pp. 88-94
  • 55
    • 35348933704 scopus 로고    scopus 로고
    • Optimal and sub-optimal quarantine and isolation control in SARS epidemics
    • Yan X, Zou Y (2008) Optimal and sub-optimal quarantine and isolation control in SARS epidemics. Math Comput Modell 47: 235-245.
    • (2008) Math Comput Modell , vol.47 , pp. 235-245
    • Yan, X.1    Zou, Y.2
  • 56
    • 39449089740 scopus 로고    scopus 로고
    • Optimal quarantine and isolation strategies in epidemics control
    • Yan X, Zou Y, Li J (2007) Optimal quarantine and isolation strategies in epidemics control. World J Modell Simul 3(3): 202-211.
    • (2007) World J Modell Simul , vol.3 , Issue.3 , pp. 202-211
    • Yan, X.1    Zou, Y.2    Li, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.