Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity

Ashrafi, 2008, Mathematical analysis of the role of repeated exposure on malaria transmission dynamics, Differ. Equat. Dyn. Syst., 16, 251, 10.1007/s12591-008-0015-1

Abdulla, 2008, Safety and immunogenicity of RTS,S/AS02 malaria vaccine in infants, N. Engl. J. Med., 359, 2533, 10.1056/NEJMoa0807773

Adams, 2004, Dynamic multidrug therapies for HIV: optimal and STI control approaches, Math. Biosci. Eng., 1, 223, 10.3934/mbe.2004.1.223

Ainseba, B., Benosman, C., 2010. Optimal control for resistance and suboptimal response in CML. Math. Biosci., 227, 81–93.

Alonso, 2004, Efficacy of the RTS,S/AS02A vaccine against Plasmodium falciparum infection and disease in young African children: randomized controlled trial, Lancet, 364, 1411, 10.1016/S0140-6736(04)17223-1

Alonso, 2005, Duration of protection with RTS,S/AS02A malaria vaccine in prevention of Plasmodium falciparum disease in Mozambican children: single-blind extended follow-up of a randomised controlled trial, Lancet, 366, 2012, 10.1016/S0140-6736(05)67669-6

Aponte, 2007, Safety of the RTS,S/AS02D candidate malaria vaccine in infants living in a highly endemic area of Mozambique: a double blind randomised controlled phase I/IIb trial, Lancet, 370, 1543, 10.1016/S0140-6736(07)61542-6

Augas, 2008, Prospects for malaria eradication in sub-Saharan Africa, PLoS One, 3, e1767, 10.1371/journal.pone.0001767

Barrett, 2007, Optimal disease eradication, Environ. Dev. Econ., 12, 627, 10.1017/S1355770X07003816

Bejon, 2008, Efficacy of RTS,S/AS01E vaccine against malaria in children 5 to 17 months of age, N. Engl. J. Med., 359, 2521, 10.1056/NEJMoa0807381

Blayneh, 2009, Optimal control of vector-borne diseases: treatment and prevention, Discrete Contin. Dyn. Syst. Ser. B, 11, 587, 10.3934/dcdsb.2009.11.587

Bojang, 2001, Efficacy of RTS,S/AS02 malaria vaccine against Plasmodium falciparum infection in semi-immune adult men in The Gambia: a randomised trial, Lancet, 358, 1927, 10.1016/S0140-6736(01)06957-4

Bojang, 2009, Five-year safety and immunogenicity of GlaxoSmithKline's candidate malaria vaccine RTS,S/AS02 following administration to semi-immune adult men living in a malaria-endemic region of The Gambia, Hum. Vaccine, 5, 242, 10.4161/hv.5.4.7050

Cesar, 2006, Optimal control of an epidemic through educational campaigns, Electron. J. Differ. Equat., 125, 1

Chiyaka, 2008, A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Appl. Math. Comput., 195, 641, 10.1016/j.amc.2007.05.016

Chiyaka, 2009, Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas, Theor. Popul. Biol., 75, 14, 10.1016/j.tpb.2008.10.002

de Souza, 2000, Optimal control theory applied to the anti-viral treatment of AIDS

Denis, 1997, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35, 775, 10.1007/s002850050076

Dietz, 1974, A malaria model tested in the African savannah, Bull. World Health Organ., 50, 347

Doedel, E.J., Paffenroth, R.C., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X., 2002. AUTO 2000: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), v.0.9.7, 2002, online at http://sourceforge.net/projects/auto2000/.

Fleming, 1975

Garba, 2008, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215, 11, 10.1016/j.mbs.2008.05.002

Goldman, 2002, Cost optimisation in the SIS model of infectious disease with treatment, Top. Econ. Anal. Policy, 2

Gumel, 2008, Existence of multiple-stable equilibria for a multi-drug-resistant model of Mycobacterium tuberculosis, Math. Biosci. Eng., 5, 437, 10.3934/mbe.2008.5.437

Gupta, 1973, Optimal control of epidemics, Math. Biosci., 18, 383, 10.1016/0025-5564(73)90012-6

Isao, 2004, Combining zooprophylaxis and insecticide spraying: a malaria-control strategy limiting the development of insecticide resistance in vector mosquitoes, Proc. R. Soc. Lond., 271, 301, 10.1098/rspb.2003.2575

Joshi, 2006, Optimal control methods applied to disease models, Contemp. Math., 410, 187, 10.1090/conm/410/07728

Joshi, 2002, Optimal control of an HIV immunology model, Optim. Control Appl. Math., 23, 199, 10.1002/oca.710

Kar, 2011, Stability analysis and optimal control of an SIR epidemic model with vaccination, Biosystems, 104, 127, 10.1016/j.biosystems.2011.02.001

Karrakchou, 2006, Optimal control and infectiology: application to an HIV/AIDS model, Appl. Math. Comput., 177, 807, 10.1016/j.amc.2005.11.092

Kirschner, 1997, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35, 775, 10.1007/s002850050076

Koella, 2003, Epidemiological models for the spread of anti-malaria resistance, Malaria J., 2, 1, 10.1186/1475-2875-2-3

Lenhart, 1992, Application of distributed parameter control model in wildlife damage management, Math. Models Methods Appl. Sci., 2, 423, 10.1142/S0218202592000259

Lenhart, 2007

Lenhart, 1997

Li, 2008, A malaria model with partial immunity in humans, Math. Biosci. Eng., 5, 789, 10.3934/mbe.2008.5.789

Lindsay, 1998, Malaria in the African highlands: past, present and future, Bull. WHO, 76, 33

Lord, 1996, Vector-borne diseases and the basic reproduction number: a case study of African horse sickness, Med. Vet. Entomol., 10, 19, 10.1111/j.1365-2915.1996.tb00077.x

Maire, 2006, Modeling a field trial of the RTS,S/AS02A malaria vaccine, Am. J. Trop. Med. Hyg., 75, 104, 10.4269/ajtmh.2006.75.104

Makinde, 2011, Impact of chemo-therapy on optimal control of malaria disease with infected immigrants, Biosystems, 104, 32, 10.1016/j.biosystems.2010.12.010

Marsh, 1998, Malaria disaster in Africa, Lancet, 352, 924, 10.1016/S0140-6736(05)61510-3

Mukandavire, 2009, Mathematical analysis of a model for HIV-malaria co-infection, Math. Biosci. Eng., 6, 333, 10.3934/mbe.2009.6.333

Mushayabasa, 2011, Modelling gonorrhea and HIV co-interaction, J. Biosyst., 103, 27, 10.1016/j.biosystems.2010.09.008

Nakul, 2006, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math., 67, 24, 10.1137/050638941

Nakul, 2008, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70, 1272, 10.1007/s11538-008-9299-0

Nanda, 2007, Optimal control of treatment in a mathematical model of chronic myelogenous leukemia, Math. Biosci., 210, 143, 10.1016/j.mbs.2007.05.003

Owusu-Agyei, 2009, Randomized controlled trial of RTS,S/AS02D and RTS,S/AS01E malaria candidate vaccines given according to different schedules in Ghanaian children, PLoS One, 4, e7302, 10.1371/journal.pone.0007302

Polhemus, 2009, Evaluation of RTS,S/AS02A and RTS,S/AS01B in adults in a high malaria transmission area, PLoS One, 4, e6465, 10.1371/journal.pone.0006465

Pontryagin, 1962

Rafikov, 2009, Optimal control strategy of malaria vector using genetically modified mosquitoes, J. Theor. Biol., 258, 418, 10.1016/j.jtbi.2008.08.006

Sacarlal, 2008, Safety of the RTS,S/AS02A malaria vaccine in Mozambican children during a Phase IIb trial, Vaccine, 26, 174, 10.1016/j.vaccine.2007.11.003

Sacarlal, 2009, Long-term safety and efficacy of the RTS,S/AS02A malaria vaccine in Mozambican children, J. Infect. Dis., 200, 329, 10.1086/600119

Sachs, 2002, A new infected global effort to control malaria, Science, 298, 122, 10.1126/science.1077900

Seierstad, 1987

Sethi, 1978, Optimal quarantine programmes for controlling an epidemic spread, J. Opl. Res. Soc., 29, 265, 10.1057/jors.1978.55

Sethi, 1978, Optimal control of some simple deterministic epidemic models, J. Opl. Res. Soc., 29, 129, 10.1057/jors.1978.27

Tumwiine, 2008, Threshhold and stability results for a malaria model in a population with protective intervention among high-risk groups, Math. Modell. Anal., 13, 443, 10.3846/1392-6292.2008.13.443-460

Van den Driessche, 2002, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29, 10.1016/S0025-5564(02)00108-6

Vásquez Pinzón, 2003, Mathematical model for the analysis of vaccination and vector control in malaria incidence, Rev. Salud Publica (Bogota), 5, 172

WHO expert committee on malaria, 20th report, WHO Regional Office of Africa, 2003.

Wickwire, 1975, A note on the optimal control of carrier-borne epidemic, J. Appl. Probab., 12, 565, 10.2307/3212871

Yang, 2000, Malaria transmission model for different levels of acquired immunity and temperature dependent parameters (vector), Rev. Saude Publica, 34, 223, 10.1590/S0034-89102000000300003

Yang, 2001, A mathematical model for malaria transmision relating global warming and local socioeconomic conditions, Rev. Saude Publica, 35, 224, 10.1590/S0034-89102001000300002

Zhixing, 2008, Backward bifurcation of an epidemic model with standard incidence rate and treatment rate, Nonlinear Anal: Real World Appl., 9, 2302, 10.1016/j.nonrwa.2007.08.009