This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Z. Feng, Z. Qiu, Z. Sang, C. Lorenzo, J. Glasser, “Modelling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy,” Mathematical Biosciences, vol. 245, no. 2, pp. 171-178, 2013.bFengZ.QiuZ.SangZ.LorenzoC.GlasserJ.“Modelling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy, ”24521711782013.b10.1016/j.mbs.2013.07.00323850537Search in Google Scholar
S. H. Kapiga, N. E. Sam, J. F. Shao, et al, “Herpes simplex virus type 2 infection among bar and hotel workers in northern Tanzania: prevalence and risk factors, ” Sexually Transmitted Diseases, vol. 30, pp. 187-192, 2003.KapigaS. H.SamN. E.ShaoJ. F.“Herpes simplex virus type 2 infection among bar and hotel workers in northern Tanzania: prevalence and risk factors, ”30187192200310.1097/00007435-200303000-0000112616132Search in Google Scholar
D. Watson-Jones, H.A. Weiss, M. Rusizoka, et al, “Effect of herpes simplex suppression on incidence of HIV among women in Tanzania, ” The New England Journal of Medicine, vol. 358, pp. 1-12, 2008.Watson-JonesD.WeissH.A.RusizokaM.“Effect of herpes simplex suppression on incidence of HIV among women in Tanzania, ”358112200810.1056/NEJMoa0800260264312618337596Search in Google Scholar
K. Jr Owusu-Edusei, H.W. Chesson, T.L. Gift, G. Tao, R. Mahajan, M.C. Ocfemia, K.C. Kent, “The estimated direct medical cost of selected sexually transmitted infections in the United States, ” Transmitted Diseases, vol. 40, no. 3, pp. 197-201, 2008.Owusu-EduseiK. JrChessonH.W.GiftT.L.TaoG.MahajanR.OcfemiaM.C.KentK.C.“The estimated direct medical cost of selected sexually transmitted infections in the United States, ”403197201200810.1097/OLQ.0b013e318285c6d223403600Search in Google Scholar
V. Lakshmikantham, S. Leela, A. A. Martynyuk, Stability analysis of nonlinear systems, Marcel Dekker, Inc., New York and Basel, 1989.LakshmikanthamV.LeelaS.MartynyukA. A.Stability analysis of nonlinear systems, Marcel DekkerNew York and Basel198910.1142/1192Search in Google Scholar
H.W. Hethcote, The mathematics of infectious diseases. SIAM Review, 42(4): 599-653, 2000.HethcoteH.W.The mathematics of infectious diseases424599653200010.1137/S0036144500371907Search in Google Scholar
A. Wald and K. Link, “Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis, ” Journal of Infectious Diseases, vol. 185, pp. 45-52, 2002.WaldA.LinkK.“Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis, ”1854552200210.1086/33823111756980Search in Google Scholar
S. Blower, L. Ma, Calculating the contribution of herpes simplex virus type 2 epidemics to increasing HIV incidence: treatment implications, Clin. Infect. Dis. 39 (Suppl 5) (2004) S240.BlowerS.MaL.Calculating the contribution of herpes simplex virus type 2 epidemics to increasing HIV incidence: treatment implications3952004S24010.1086/42236115494895Search in Google Scholar
R. S. McClelland, C. C. Wang, J. Overbaugh, et al, “Association between cervical shedding of herpes simplex virus and HIV-1, ” AIDS, vol. 16, no. 18, pp. 2425-2430, 2002.McClellandR. S.WangC. C.OverbaughJ.“Association between cervical shedding of herpes simplex virus and HIV-1, ”161824252430200210.1097/00002030-200212060-0000712461416Search in Google Scholar
C. Tanton, H. A. Weiss, M. Rusizoka, et al. “Long term impact of acyclovir suppressive therapy on genital and plasma HIV RNA in Tanzanian women: a randomized controlled trial, ” Journal of Infectious Diseases, vol. 201, no. 9, pp. 1285-1297, 2010.TantonC.WeissH. A.RusizokaM.“Long term impact of acyclovir suppressive therapy on genital and plasma HIV RNA in Tanzanian women: a randomized controlled trial, ”201912851297201010.1086/651696294853620235836Search in Google Scholar
M. L. Plummer, D. Watson-Jones, S. Lees, K. Baisley, S. Matari, J. Changalucha, T. Clayton, K. Mugeye, C. Tanton, W. A. Weiss, D.A. Ross, R.J. Hayes, “A qualitative study of participant adherence in a randomized controlled trial of herpes suppressive therapy for HIV prevention in Tanzania, ” AIDS Care, vol. 22, no. 4, pp. 499-508, 2010.PlummerM. L.Watson-JonesD.LeesS.BaisleyK.MatariS.ChangaluchaJ.ClaytonT.MugeyeK.TantonC.WeissW. A.RossD.A.HayesR.J.“A qualitative study of participant adherence in a randomized controlled trial of herpes suppressive therapy for HIV prevention in Tanzania, ”224499508201010.1080/09540120903202889Search in Google Scholar
F. X. Mbopi-Keou, G. Gresenguet, P. Mayaud, H. A. Weiss, R. Gopal, M. Matta, et al. “Interactions between herpes simplex virus type 2 and human immunodeficiency virus type 1 infection in African women: opportunities for intervention, ” Journal of Infectious Diseases, vol. 182, no. 4, pp. 1090-1096, 2000.Mbopi-KeouF. X.GresenguetG.MayaudP.WeissH. A.GopalR.MattaM.“Interactions between herpes simplex virus type 2 and human immunodeficiency virus type 1 infection in African women: opportunities for intervention, ”182410901096200010.1086/315836Search in Google Scholar
S.J. Reynolds and T.C. Quinn, “Developments in STD/HIV interactions the intertwining epidemics of HIV and HSV-2, ” Infect Disease Clinics of North America, vol. 19, pp. 415-425, 2005.ReynoldsS.J.QuinnT.C.“Developments in STD/HIV interactions the intertwining epidemics of HIV and HSV-2, ”19415425200510.1016/j.idc.2005.04.005Search in Google Scholar
S. M. Blower, P. T. Porco, G. Garby, “Predicting and preventing the emergence of antiviral drug resistance in HSV-2,” Nature Medicine, vol. 4, no. 6, pp. 673, 1998.BlowerS. M.PorcoP. T.GarbyG.“Predicting and preventing the emergence of antiviral drug resistance in HSV-2, ”46673199810.1038/nm0698-673Search in Google Scholar
P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29-48, 2002.van den DriesscheP.WatmoughJ.“Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission, ”1801-22948200210.1016/S0025-5564(02)00108-6Search in Google Scholar
C. Alvey, Z. Feng, J. Glasser, “A model for the coupled disease dynamics of HIV and HSV-2 with mixing among and between genders, ” Mathematical Biosciences, vol. 265, pp. 82-100, 2015.AlveyC.FengZ.GlasserJ.“A model for the coupled disease dynamics of HIV and HSV-2 with mixing among and between genders, ”26582100201510.1016/j.mbs.2015.04.00925953482Search in Google Scholar
E. E. Freeman, R. G. White, R. Bakker, K. K. Orroth, A. H. Weiss, A. Buv, R. J. Hayes, J. R. Glynna, “Population-level effect of potential HSV-2 prophylactic vaccines on HIV incidence in sub-Saharan Africa, ” Vaccine, vol. 27, no. 6, pp. 940-946, 2006.FreemanE. E.WhiteR. G.BakkerR.OrrothK. K.WeissA. H.BuvA.HayesR. J.GlynnaJ. R.“Population-level effect of potential HSV-2 prophylactic vaccines on HIV incidence in sub-Saharan Africa, ”276940946200610.1016/j.vaccine.2008.11.074268608019071187Search in Google Scholar
G. Kapitanov, C. Alvey, K. Vogt-Geisse, Z. Feng, “An Age-Structured Model For the Coupled Dynamics of HIV and HSV-2, ”. Mathematical Biosciences and Engineering, vol. 12, no. 4, pp. 803-840, 2015.KapitanovG.AlveyC.Vogt-GeisseK.FengZ.“An Age-Structured Model For the Coupled Dynamics of HIV and HSV-2, ”124803840201510.3934/mbe.2015.12.80325974346Search in Google Scholar
R.G. White, E.E. Freeman, K.K. Orroth, R. Bakker, H.A. Weiss, et al., “Population level effect of HSV-2 therapy on the incidence of HIV in sub-Saharan Africa, ” Sexually Transmitted Infections, vol. 84, no. 2, pp. ii12, 2008.WhiteR.G.FreemanE.E.OrrothK.K.BakkerR.WeissH.A.“Population level effect of HSV-2 therapy on the incidence of HIV in sub-Saharan Africa, ”842ii12200810.1136/sti.2008.029918260275218799486Search in Google Scholar
Z. Mukandavire, A.B. Gumel, W. Garira, J.M. Tchuenche, “Mathematical analysis of a model for HIV-Malaria co-infection, ” Mathematical biosciences and engineering, vol. 6, no. 2, 2009, pp. 333-361.MukandavireZ.GumelA.B.GariraW.TchuencheJ.M.“Mathematical analysis of a model for HIV-Malaria co-infection, ”62200933336110.3934/mbe.2009.6.33319364156Search in Google Scholar
A. Mhlanga, C.P. Bhunu, S. Mushayabasa, “A computational study of HSV-2 with poor treatment adherence, ” Abstract and applied analysis, Article ID (850670), 15 pages, 2015, http://dx.doi.org/10.1155/2015/850670.MhlangaA.BhunuC.P.MushayabasaS.“A computational study of HSV-2 with poor treatment adherence, ”Article ID (850670)152015http://dx.doi.org/10.1155/2015/85067010.1155/2015/850670Search in Google Scholar
C. Castillo-Chavez, Z. Feng, and W. Huang, On the computation of R0 and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory, C. Castillo-Chavez et al., Ed., IMA, 126, pp. 215-230, Springer, 2002.Castillo-ChavezC.FengZ.HuangW.On the computation of R0 and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious DiseasesIMA126215230Springer200210.1007/978-1-4757-3667-0_13Search in Google Scholar
C. Castillo-Chavez, B. Song, “Dynamical models of tuberculosis and their applications,” Mathematical Biosciences and Engineering, vol. 1, no. 2, pp. 361-404, 2004.Castillo-ChavezC.SongB.“Dynamical models of tuberculosis and their applications, ”12361404200410.3934/mbe.2004.1.361Search in Google Scholar
A.M. Foss, P.T. Vickerman, Z. Chalabi, P. Mayaud, M. Alary, C.H. Watts, “Dynamic modelling of herpes simplex virus type-2 (HSV-2) transmission: issue in structure uncertainty,” Bulletin of mathematical biology, vol. 71, no. 3, pp. 720-749, 2009.FossA.M.VickermanP.T.ChalabiZ.MayaudP.AlaryM.WattsC.H.“Dynamic modelling of herpes simplex virus type-2 (HSV-2) transmission: issue in structure uncertainty, ”713720749200910.1007/s11538-008-9379-1Search in Google Scholar
L.J. Abu-Raddad, A.S. Magaret, C. Celum et al., “Genital herpes has played a more important role than any other sexually transmitted infections in driving HIV prevalence in Africa,” Plos One, vol. 3, no. 5, pp. e2230, 2008.Abu-RaddadL.J.MagaretA.S.CelumC.“Genital herpes has played a more important role than any other sexually transmitted infections in driving HIV prevalence in Africa, ”35e2230200810.1371/journal.pone.0002230Search in Google Scholar
D. R. Bangsberg, S. Perry, E. D. Charlebois, R. A. Clark, M. Roberston, A. R. Zolopa, A. Moss, “Non-adherence to highly active antiretroviral therapy predicts progression to AIDS,” Aids, vol. 15, no. 9, pp. 1181-1183, 2001.BangsbergD. R.PerryS.CharleboisE. D.ClarkR. A.RoberstonM.ZolopaA. R.MossA.“Non-adherence to highly active antiretroviral therapy predicts progression to AIDS, ”15911811183200110.1097/00002030-200106150-00015Search in Google Scholar
C. E. Golin, H. Liu, R. D. Hays, L. G. Miller, C. K. Beck, J. Ickovics, A. H. Kaplan, N. S. Wenger, “A prospective study of predictors of adherence to combination antiretroviral medication,” Journal of general internal medicine, vol. 17, no. 10, pp. 756-65, 2002.GolinC. E.LiuH.HaysR. D.MillerL. G.BeckC. K.IckovicsJ.KaplanA. H.WengerN. S.“A prospective study of predictors of adherence to combination antiretroviral medication, ”171075665200210.1046/j.1525-1497.2002.11214.xSearch in Google Scholar
A. Wald and K. Link, “Risk of human immunodeficiency virus infection in Herpes simplex virus type 2-seropositive persons: a meta-analysis,” Journal of Infectious Diseases, vol. 185, pp. 45, 2002.WaldA.LinkK.“Risk of human immunodeficiency virus infection in Herpes simplex virus type 2-seropositive persons: a meta-analysis18545200210.1086/338231Search in Google Scholar
J.C. Helton, “Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, ” Reliability Engineering and System Saftey, vol. 42, pp. 327-367, 1993.HeltonJ.C.“Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, ”42327367199310.1016/0951-8320(93)90097-ISearch in Google Scholar
E.E. Freeman, H.A. Weiss, J.R. Glynn, P.L. Cross, J.A. Whitworth, R.J. Hayes, Herpes simplex virus 2 infection increases HIV acquisition in men and women: systematic review and meta-analysis of longitudinal studies, AIDS 20 (2006) 73.FreemanE.E.WeissH.A.GlynnJ.R.CrossP.L.WhitworthJ.A.HayesR.J.Herpes simplex virus 2 infection increases HIV acquisition in men and women: systematic review and meta-analysis of longitudinal studies2020067310.1097/01.aids.0000198081.09337.a716327322Search in Google Scholar
C. P. Bhunu, W. Garira, Z. Mukandavire, “Modelling HIV/AIDS and tuberculosis coinfection,” Bulletin of Mathematical Biology vol. 71, pp. 1745-1780, 2009.BhunuC. P.GariraW.MukandavireZ.“Modelling HIV/AIDS and tuberculosis coinfection, ”7117451780200910.1007/s11538-009-9423-919475456Search in Google Scholar
W. Fleming and R. Rishel, Deterministic and Stochastic optimal control, Springer, 1975. http://cds.cern.ch/record/1611958.FlemingW.RishelR.Springer1975http://cds.cern.ch/record/161195810.1007/978-1-4612-6380-7Search in Google Scholar
L.S. Pontryagin, Mathematical theory of Optimal Processes, Interscience Publishers John Wiley and Sons, Inc., New York, London, 1962.PontryaginL.S.Interscience Publishers John Wiley and Sons, Inc.New York, London1962Search in Google Scholar
J. Carr, Applications of centre manifold theory, Springer-Verlag, New York, 1981.CarrJ.Springer-VerlagNew York198110.1007/978-1-4612-5929-9Search in Google Scholar
S. Lenhart, J.T. Workman. Optimal control applied to biological models, Chapman and Hall, London, 2007.LenhartS.WorkmanJ.T.Optimal control applied to biological modelsLondon200710.1201/9781420011418Search in Google Scholar
O. Sharomi, A.B. Gumel, “Curtailing smoking dynamics: A mathematical modeling approach, ” Applied Mathematics and Computations, vol. 195, pp. 475-499, 2007.SharomiO.GumelA.B.“Curtailing smoking dynamics: A mathematical modeling approach, ”195475499200710.1016/j.amc.2007.05.012Search in Google Scholar
S. Mushayabasa, J.M. Tchuenche, C.P. Bhunu, E. Ngarakana-Gwasira, “Modeling gonorrhea and HIV co-interaction, ” BioSystems, vol. 103, pp. 27-37, 2011.MushayabasaS.TchuencheJ.M.BhunuC.P.Ngarakana-GwasiraE.“Modeling gonorrhea and HIV co-interaction, ”1032737201110.1016/j.biosystems.2010.09.00820869424Search in Google Scholar
V. Lakshmikantham, S. Leela. A.A. Martynyuk, Stability analysis of nonlinear systems, Marcel Dekker, New York, 1989. ISBN 0-8247-8067-1. Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 125.LakshmikanthamV.LeelaS.MartynyukA.A.Stability analysis of nonlinear systemsMarcel DekkerNew York1989ISBN 0-8247-8067-1125Search in Google Scholar
G. Magombedze, W. Garira, E. Mwenje, C.P. Bhunu, “Optimal control for HIV-1 triple therapy, ” International Journal of Computer Mathematics, vol. 88, pp. 314-340, 2011.MagombedzeG.GariraW.MwenjeE.BhunuC.P.“Optimal control for HIV-1 triple therapy, ”88314340201110.1080/00207160903443755Search in Google Scholar