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Volumn 111, Issue 2, 2013, Pages 83-101

Optimal control strategies and cost-effectiveness analysis of a malaria model

Author keywords

Backward bifurcation; Cost effectiveness; Malaria; Optimal control; Sensitivity index; Stability

Indexed keywords

ANTIMALARIAL AGENT; INSECTICIDE;

EID: 84872670823     PISSN: 03032647     EISSN: 18728324     Source Type: Journal    
DOI: 10.1016/j.biosystems.2012.09.008     Document Type: Article
Times cited : (179)

References (53)
  • 1
    • 28544448294 scopus 로고    scopus 로고
    • Dynamic multidrug therapies for HIV: optimal and STI control approaches
    • Adams B.M., Banks H.T., Kwon H., Tran H.T. Dynamic multidrug therapies for HIV: optimal and STI control approaches. Math. Biosci. Eng. 2004, 1(2):223-241.
    • (2004) Math. Biosci. Eng. , vol.1 , Issue.2 , pp. 223-241
    • Adams, B.M.1    Banks, H.T.2    Kwon, H.3    Tran, H.T.4
  • 3
    • 80054854637 scopus 로고    scopus 로고
    • Mathematical analysis of the role of repeated exposure on malaria transmission dynamics
    • Ashrafi M.N., Gumel A.B. Mathematical analysis of the role of repeated exposure on malaria transmission dynamics. Differ. Equat. Dynam. Syst. 2008, 16(3):251-287.
    • (2008) Differ. Equat. Dynam. Syst. , vol.16 , Issue.3 , pp. 251-287
    • Ashrafi, M.N.1    Gumel, A.B.2
  • 4
    • 33748307685 scopus 로고    scopus 로고
    • Dynamical models of tuberculosis and their applications
    • Castillo-Chavez C., Song B. Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 2004, 1(2):361-404.
    • (2004) Math. Biosci. Eng. , vol.1 , Issue.2 , pp. 361-404
    • Castillo-Chavez, C.1    Song, B.2
  • 5
    • 37349003324 scopus 로고    scopus 로고
    • Mathematical analysis of the effects of control strategies on the transmission dynamics of malaria
    • Chiyaka C., Tchuenche J.M., Garira W., Dube S.A. Mathematical analysis of the effects of control strategies on the transmission dynamics of malaria. Appl. Math. Comput. 2008, 195:641-662.
    • (2008) Appl. Math. Comput. , vol.195 , pp. 641-662
    • Chiyaka, C.1    Tchuenche, J.M.2    Garira, W.3    Dube, S.A.4
  • 6
    • 58249127281 scopus 로고    scopus 로고
    • Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas
    • Chiyaka C., Garira W., Dube S. Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas. Theor. Popul. Biol. 2009, 75:14-29.
    • (2009) Theor. Popul. Biol. , vol.75 , pp. 14-29
    • Chiyaka, C.1    Garira, W.2    Dube, S.3
  • 7
    • 85194537204 scopus 로고    scopus 로고
    • Division of parasitic diseases, National Center for Infectious Diseases, Center for Disease Control and Prevention (CDC), USA.
    • Division of parasitic diseases, National Center for Infectious Diseases, Center for Disease Control and Prevention (CDC), USA.
  • 12
    • 49849105967 scopus 로고    scopus 로고
    • Backward bifurcations in dengue transmission dynamics
    • Garba S.M., Gumel A.B., Abu B. Backward bifurcations in dengue transmission dynamics. Math. Biosci. 2008, 215:11-25.
    • (2008) Math. Biosci. , vol.215 , pp. 11-25
    • Garba, S.M.1    Gumel, A.B.2    Abu, B.3
  • 13
    • 52049112576 scopus 로고    scopus 로고
    • Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis
    • Gumel A.B., Song B. Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis. Math. Biosci. Eng. 2008, 5(3):437-455.
    • (2008) Math. Biosci. Eng. , vol.5 , Issue.3 , pp. 437-455
    • Gumel, A.B.1    Song, B.2
  • 14
    • 0015722857 scopus 로고
    • Optimal control of epidemics
    • Gupta N.K., Rink R.E. Optimal control of epidemics. Math. Biosci. 1973, 18:383-396.
    • (1973) Math. Biosci. , vol.18 , pp. 383-396
    • Gupta, N.K.1    Rink, R.E.2
  • 15
    • 0034201149 scopus 로고    scopus 로고
    • Malaria transmission model for different levels of acquired immunity and temperature dependent parameters (vector)
    • Hyun M.Y. Malaria transmission model for different levels of acquired immunity and temperature dependent parameters (vector). Rev. Saude Publica 2000, 34(3):223-231.
    • (2000) Rev. Saude Publica , vol.34 , Issue.3 , pp. 223-231
    • Hyun, M.Y.1
  • 16
    • 0035376473 scopus 로고    scopus 로고
    • A mathematical model for malaria transmission relating global warming and local socioeconomic conditions
    • Hyun M.Y. A mathematical model for malaria transmission relating global warming and local socioeconomic conditions. Rev. Saude Publica 2001, 35(3):224-231.
    • (2001) Rev. Saude Publica , vol.35 , Issue.3 , pp. 224-231
    • Hyun, M.Y.1
  • 17
    • 1042302717 scopus 로고    scopus 로고
    • Combining zooprophylaxis and insecticide spraying: a malaria-control strategy limiting the development of insecticide resistance in vector mosquitoes
    • Isao K., Akira S., Motoyoshi M. Combining zooprophylaxis and insecticide spraying: a malaria-control strategy limiting the development of insecticide resistance in vector mosquitoes. Proc. R. Soc. Lond. 2004, 271:301-309.
    • (2004) Proc. R. Soc. Lond. , vol.271 , pp. 301-309
    • Isao, K.1    Akira, S.2    Motoyoshi, M.3
  • 18
    • 58849150466 scopus 로고    scopus 로고
    • A malaria model with partial immunity in humans
    • Jia L. A malaria model with partial immunity in humans. Math. Biosci. Eng. 2008, 5(4):789-801.
    • (2008) Math. Biosci. Eng. , vol.5 , Issue.4 , pp. 789-801
    • Jia, L.1
  • 19
    • 0036631015 scopus 로고    scopus 로고
    • Optimal control of an HIV immunology model
    • Joshi H.R. Optimal control of an HIV immunology model. Optim. Control Appl. Math. 2002, 23:199-213.
    • (2002) Optim. Control Appl. Math. , vol.23 , pp. 199-213
    • Joshi, H.R.1
  • 20
    • 77951691230 scopus 로고    scopus 로고
    • Optimal control methods applied to disease models
    • Joshi H.R., Lenhart S., Li M.Y., Wang L. Optimal control methods applied to disease models. Contemp. Math. 2006, 410:187-207.
    • (2006) Contemp. Math. , vol.410 , pp. 187-207
    • Joshi, H.R.1    Lenhart, S.2    Li, M.Y.3    Wang, L.4
  • 21
    • 0042762770 scopus 로고    scopus 로고
    • Optimal control of treatments in a two-strain tuberculosis model
    • Jung E., Lenhart S., Feng Z. Optimal control of treatments in a two-strain tuberculosis model. Discrete Continuous Dynam. Syst. Ser. B 2002, 2(4):473-482.
    • (2002) Discrete Continuous Dynam. Syst. Ser. B , vol.2 , Issue.4 , pp. 473-482
    • Jung, E.1    Lenhart, S.2    Feng, Z.3
  • 22
    • 79953753536 scopus 로고    scopus 로고
    • Stability analysis and optimal control of an SIR epidemic model with vaccination
    • Kar T.K., Batabyal A. Stability analysis and optimal control of an SIR epidemic model with vaccination. Biosystems 2011, 104(2-3):127-135.
    • (2011) Biosystems , vol.104 , Issue.2-3 , pp. 127-135
    • Kar, T.K.1    Batabyal, A.2
  • 23
    • 33744999665 scopus 로고    scopus 로고
    • Optimal control and infectiology: application to an HIV/AIDS model
    • Karrakchou J., Rachik M., Gourari S. Optimal control and infectiology: application to an HIV/AIDS model. Appl. Math. Comput. 2006, 177:807-818.
    • (2006) Appl. Math. Comput. , vol.177 , pp. 807-818
    • Karrakchou, J.1    Rachik, M.2    Gourari, S.3
  • 25
    • 0031204179 scopus 로고    scopus 로고
    • Optimal control of the chemotherapy of HIV
    • Kirschner D., Lenhart S., Serbin S. Optimal control of the chemotherapy of HIV. J. Math. Biol. 1997, 35:775-792.
    • (1997) J. Math. Biol. , vol.35 , pp. 775-792
    • Kirschner, D.1    Lenhart, S.2    Serbin, S.3
  • 26
    • 85044704133 scopus 로고    scopus 로고
    • Epidemiological models for the spread of anti-malaria resistance
    • Koella J.C., Anita R. Epidemiological models for the spread of anti-malaria resistance. Malar. J. 2003, 2:3.
    • (2003) Malar. J. , vol.2 , pp. 3
    • Koella, J.C.1    Anita, R.2
  • 29
    • 15044356735 scopus 로고
    • Optimal Control for Degenerate Parabolic Equations with Logistic Growth
    • Lenhart S., Yong J. Optimal Control for Degenerate Parabolic Equations with Logistic Growth. Nonlinear Anal. 1995, 25:681-698.
    • (1995) Nonlinear Anal. , vol.25 , pp. 681-698
    • Lenhart, S.1    Yong, J.2
  • 30
    • 76549258856 scopus 로고
    • The analysis of infection rates in diseases in which superinfection occurs
    • Macdonald G. The analysis of infection rates in diseases in which superinfection occurs. Trop. Dis. Bull. 1950, 47:907-915.
    • (1950) Trop. Dis. Bull. , vol.47 , pp. 907-915
    • Macdonald, G.1
  • 32
    • 0035265524 scopus 로고    scopus 로고
    • Optimal and suboptimal control in dengue epidemics
    • Marco A.L.C., Takashi Y. Optimal and suboptimal control in dengue epidemics. Optim. Control Appl. Methods 2001, 22:63-73.
    • (2001) Optim. Control Appl. Methods , vol.22 , pp. 63-73
    • Marco, A.L.C.1    Takashi, Y.2
  • 34
    • 79961127459 scopus 로고    scopus 로고
    • Mathematical analysis of a cholera model with public health interventions
    • Mwasa A., Tchuenche J.M. Mathematical analysis of a cholera model with public health interventions. Biosystems 2011, 105(3):190-200.
    • (2011) Biosystems , vol.105 , Issue.3 , pp. 190-200
    • Mwasa, A.1    Tchuenche, J.M.2
  • 35
    • 33847746157 scopus 로고    scopus 로고
    • Bifurcation analysis of a mathematical model for malaria transmission
    • Nakul C., Cushing J.M., Hyman J.M. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math. 2006, 67(1):24-45.
    • (2006) SIAM J. Appl. Math. , vol.67 , Issue.1 , pp. 24-45
    • Nakul, C.1    Cushing, J.M.2    Hyman, J.M.3
  • 36
    • 47349102730 scopus 로고    scopus 로고
    • Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model
    • Nakul C., Hyman J.M., Cushing J.M. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol. 2008, 70:1272-1296.
    • (2008) Bull. Math. Biol. , vol.70 , pp. 1272-1296
    • Nakul, C.1    Hyman, J.M.2    Cushing, J.M.3
  • 37
    • 0033752986 scopus 로고    scopus 로고
    • A mathematical model for endemic malaria with variable human and mosquito population
    • Ngwa G.A., Shu W.S. A mathematical model for endemic malaria with variable human and mosquito population. Math. Comput. Model. 2000, 32:747-763.
    • (2000) Math. Comput. Model. , vol.32 , pp. 747-763
    • Ngwa, G.A.1    Shu, W.S.2
  • 38
    • 33750715725 scopus 로고    scopus 로고
    • On the population dynamics of the malaria vector
    • Ngwa G.A. On the population dynamics of the malaria vector. Bull. Math. Biol. 2006, 68:2161-2189.
    • (2006) Bull. Math. Biol. , vol.68 , pp. 2161-2189
    • Ngwa, G.A.1
  • 39
    • 80054851833 scopus 로고    scopus 로고
    • Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity
    • Okosun K.O., Ouifki R., Marcus N. Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. Biosystems 2011, 106:136-145.
    • (2011) Biosystems , vol.106 , pp. 136-145
    • Okosun, K.O.1    Ouifki, R.2    Marcus, N.3
  • 41
    • 65549154257 scopus 로고    scopus 로고
    • Optimal control of tuberculosis with exogenous reinfection
    • Rachik H.M., Saadi S., Tabit Y., Yousfi N. Optimal control of tuberculosis with exogenous reinfection. Appl. Math. Sci. 2009, 3(5):231-240.
    • (2009) Appl. Math. Sci. , vol.3 , Issue.5 , pp. 231-240
    • Rachik, H.M.1    Saadi, S.2    Tabit, Y.3    Yousfi, N.4
  • 42
    • 67349120283 scopus 로고    scopus 로고
    • Optimal control strategy of malaria vector using genetically modified mosquitoes
    • Rafikov M., Bevilacqua L., Wyse A.P.P. Optimal control strategy of malaria vector using genetically modified mosquitoes. J. Theor. Biol. 2009, 258:418-425.
    • (2009) J. Theor. Biol. , vol.258 , pp. 418-425
    • Rafikov, M.1    Bevilacqua, L.2    Wyse, A.P.P.3
  • 43
    • 53849118810 scopus 로고    scopus 로고
    • Determining effective spraying periods to control malaria via indoor residual spraying in sub-Saharan Africa
    • doi:10.1155/2008/745463, Article ID 745463, Hindawi Publishing Corporation.
    • Robert, J.S., Hove-Musekwa, S.D., 2008. Determining effective spraying periods to control malaria via indoor residual spraying in sub-Saharan Africa. J. Appl. Math. Decis. Sci. 19 pp., doi:10.1155/2008/745463, Article ID 745463, Hindawi Publishing Corporation.
    • (2008) J. Appl. Math. Decis. Sci. , pp. 19
    • Robert, J.S.1    Hove-Musekwa, S.D.2
  • 45
    • 0037020026 scopus 로고    scopus 로고
    • A new infected global effort to control malaria
    • doi:10.1126/science
    • Sachs J.D. A new infected global effort to control malaria. Science 2002, 298:122-124. doi:10.1126/science.
    • (2002) Science , vol.298 , pp. 122-124
    • Sachs, J.D.1
  • 46
    • 84974870159 scopus 로고
    • Optimal quarantine programmes for controlling an epidemic spread
    • (Pergamon Press)
    • Suresh P.S. Optimal quarantine programmes for controlling an epidemic spread. J. Oper. Res. Soc. 1978, 29(3):265-268. (Pergamon Press).
    • (1978) J. Oper. Res. Soc. , vol.29 , Issue.3 , pp. 265-268
    • Suresh, P.S.1
  • 47
    • 84974873238 scopus 로고
    • Optimal control of some simple deterministic epidemic models
    • (Pergamon Press)
    • Suresh P.S. Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc. 1978, 29(2):129-136. (Pergamon Press).
    • (1978) J. Oper. Res. Soc. , vol.29 , Issue.2 , pp. 129-136
    • Suresh, P.S.1
  • 48
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • Van den D.P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 2002, 180:29-48.
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • Van den, D.P.1    Watmough, J.2
  • 49
    • 0017481192 scopus 로고
    • Mathematical models for the control of pests and infectious diseases: survey
    • Wickwire K. Mathematical models for the control of pests and infectious diseases: survey. Theor. Popul. Biol. 1977, 11:182-238.
    • (1977) Theor. Popul. Biol. , vol.11 , pp. 182-238
    • Wickwire, K.1
  • 50
    • 0023519121 scopus 로고
    • Optimal disease control through combined use of preventive and curative measures
    • (North-Holland)
    • Wiemer C. Optimal disease control through combined use of preventive and curative measures. J. Dev. Econ. 1987, 25:301-319. (North-Holland).
    • (1987) J. Dev. Econ. , vol.25 , pp. 301-319
    • Wiemer, C.1
  • 51
    • 39449089740 scopus 로고    scopus 로고
    • Optimal quarantine and isolation strategies in epidemics control
    • Xiefei Y., Yun Z., Jianliang L. Optimal quarantine and isolation strategies in epidemics control. World J. Model. Simul. 2007, 3(3):202-211.
    • (2007) World J. Model. Simul. , vol.3 , Issue.3 , pp. 202-211
    • Xiefei, Y.1    Yun, Z.2    Jianliang, L.3
  • 52
    • 48049122424 scopus 로고    scopus 로고
    • Stability analysis and optimal vaccination of an SIR epidemic model
    • Zaman G., Yong H.K., Jung I.H. Stability analysis and optimal vaccination of an SIR epidemic model. Biosystems 2008, 93:240-249.
    • (2008) Biosystems , vol.93 , pp. 240-249
    • Zaman, G.1    Yong, H.K.2    Jung, I.H.3
  • 53
    • 48249128675 scopus 로고    scopus 로고
    • Backward bifurcation of an epidemic model with standard incidence rate and treatment rate
    • Zhixing H., Sheng L., Hui W. Backward bifurcation of an epidemic model with standard incidence rate and treatment rate. Nonlinear Anal. Real World Appl. 2008, 9:2302-2312.
    • (2008) Nonlinear Anal. Real World Appl. , vol.9 , pp. 2302-2312
    • Zhixing, H.1    Sheng, L.2    Hui, W.3


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