Abstract
Human immunodeficiency virus (HIV) causes severe damage of human immune system. It helps to spread the disease acquired immune deficiency syndrome (AIDS) which is a serious problem facing the human race. Thus we need serious and prompt consideration to articulate some potential treatment strategies against the disease HIV/AIDS. Our fundamental focus is to study the various mathematical models using different drugs to control the HIV/AIDS disease transmission along with available anecdotal evidences in global pharmacological practices.
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References
Nowak, M.A., May, R.M.: AIDS pathogenesis: mathematical models of HIV and SIV infections. AIDS 7, S3–S18 (1993)
Bonhoeffer, S., Coffin, J.M., Nowak, M.A.: Human immunodeficiency virus drug therapy and virus load. J. Virol. 71, 3275–3278 (1997)
Kalamas, S.A., Goulder, P.J., Shea, A.K., Jones, N.G., Trocha, A.K., Ogg, G.S., Walke, B.D.: Levels of human immunodeficiency virus type 1-specific cytotoxic T-lymphocyte effector and memory responses decline after suppression of viremia with highly active antiretroviral therapy. J. Virol. 73, 6721–6728 (1999)
Layne, S.P., Spouge, J.L., Dembo, M.: Quantifying the infectivity of human immunodeficiency virus. Proc. Nat. Acad. Sci. USA 86, 4644 (1989)
Larder, B.A., Kemp, S.D., Harrigan, P.R.: Potential mechanism for sustained antiretroviral efficiency of AZT-3TC combination therapy. Sci. 269, 696–699 (1995)
Murray, J.M., Kaufmann, A.D., Kelleher, D.A.: A model of primary HIV infection. Math. Biosc. 154, 57–85 (1998)
Nowak, MA., May, R.M.: Virus Dynamics, Cambridge University Press, Cambridge, UK.112 (2000)
Perelson, A.S., Krischner, D.E., De-Boer, R.: Dynamics of HIV infection of CD4 T cells. Math. Biosc. 114, 81–125 (1993)
Perelson, A.S., Neuman, A.U., Markowitz, J.M.: Leonard, Ho, D.D.: HIV 1 dynamics in vivo: viron clearance rate, infected cell life span, and viral generation time. Science 271, 1582–1586 (1996)
Lobritz, M.A., Ratcliff, A.N., Arts, E.J.: HIV-1 entry, inhibitors, and resistance. Viruses 2, 1069–1105 (2010)
Robert, W., Trono, D.: The plasma membrane as a combat zone in the HIV battlefield. Genes Dev 14, 2677–2688 (2000)
Xiao, D., Bossert, W.H.: An intra-host mathematical model on interaction between HIV and malaria. Bull. Math. Biol. 72, 1892–1911 (2010)
Banchereau, J., Steinman, R.M.: Dendritic cells and the control of immunity. Nature 392, 245–252 (1998)
Banchereau, J., Briere, F., Caux, C., Davoust, J., Lebecque, S., Liu, Y.T., Pulendran, B., Palucka, K.: Immunobiology of dendritic cells. Annu. Rev. Immunol. 18, 767–811 (2000)
Steinman, R.M., Adams, J.C., Cohn, Z.A.: Identification of a novel cell type in peripheral lymphoid organs of mice identification and distribution in mouse spleen. J. Exp. Med. 141, 804–820 (1975)
Donaghy, H., Gazzard, B., Gotch, F., Patterson, S.: Dysfunction and infection of freshly isolated blood myeloid and plasmacytoid dendritic cells in patients infected with HIV-1. BLOOD 101(11), 4506–4511 (2003)
Townsend, A., Bodmer, H.: Antigen recognition by class Irestricted T lymphocytes. Annu. Rev. Immunol. 7, 601–624 (1989)
York, I., Rock, K.: Antigen processing and presentation by the class I major histocompatibility complex. Annu. Rev. Immunol. 14, 369–396 (1996)
Purbhoo, M., Sewell, A.K., Klenerman, P.: Copresentation of natural HIV-1 agonist and antagonist ligands fails to induce the T cell receptor signaling cascade. Proc. Natl. Acad. Sci. USA 95, 4527–4532 (1998)
Weiss, A., Littman, D.: Signal transduction by lymphocyte antigen receptors. Cell 76, 263–274 (1994)
Wange, R., Samelson, L.: Complex complexes: signaling at the TCR. Immunity 5, 197–205 (1996)
Berke, G.: The CTL’s kiss of death. Cell 81, 9–12 (1995)
Sewell, A.K., Price, D.A., Oxenius, A., Kelleher, A.D., Phillips, R.E.: Cytotoxic T lymphocyte responses to human immunodeficiency virus: control and escape. Stem Cells 18, 233–244 (2000)
Tschopp, J., Hofmann, K.: Cytotoxic T cells: more weapons for new targets? Trends Microbiol. 4, 91–94 (1996)
Culshaw, R.V., Ruan, S.: A delay-differentianal equation model of HIV infection of CD4\(^{+}\)T-cells. Math. Biosci. 165, 425–444 (2000)
Garciá, J.A., Soto-Ramirez, L.E., Cocho, G., Govezensky, T., José, M.V.: HIV-1 dynamics at different time scales under antiretroviral therapy. J. Theor. Biol. 238, 220–229 (2006)
Coffin, J.M.: HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy. Sci. 267, 482–489 (1995)
Callaway, D.S., Perelson, A.S.: HIV-1 infection and low virul loads. Bull. Math. Biol. 64, 29–64 (2002)
Culshaw, R.V., Rawn, S., Spiteri, R.J.: Optimal HIV treatment by maximising immuno response. J. Math. Biol. 48, 545–562 (2004)
Zurakowski, R., Teel, A.R.: A model predictive control based scheduling method for HIV therapy. J. Theor. Biol. 238, 368–382 (2006)
Kirschner, D.E., Webb, G.F.: A model of treatment strategy in the chemotherapy of AIDS. Bull. Math. Biol. 58, 167–190 (1996)
Perelson, A.S., Nelson, P.W.: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Theor. 41, 3–41 (1999)
Altes, H.K., Wodarz, D., Jansen, V.A.A.: The dual role of CD4T helper cells in the infection dynamics of HIV and their importance for vaccination. J. Theor. Biol. 214, 633–644 (2002)
Skim, H., Han, S.J., Chung, C.C., Nan, S.W., Seo, J.H.: Optimal scheduling of drug trement for HIV infection. Int. J. Control, Autom. Syst. 1(3), 282–288 (2003)
Wodarz, D., Nowak, M.A.: Specific therapy regimes could lead to long-term immunological control to HIV. Proc. Natl. Acad. Sci. USA 96(25), 14464–14469 (1999)
Wodarz, D., May, R.M., Nowak, M.A.: The role of antigen-independent persistence of memory cytotoxic T lymphocytes. Int. Immunol. 12(A), 467–477 (2000)
Adams, B.M., Banks, H.T., Kwon, H.D., Tran, H.T.: Dynamic multidrug therapies for HIV: optimal and STI control approaches. Biosci. Eng. 1, 223–242 (2004)
Kim, W.H., Chung, H.B., Chung, C.C.: Optimal switching in structured treatment interruption for HIV therapy. Asian J. Control. 8(3), 290–296 (2006)
Kwon, H.D.: Optimal treatment strategies derived from a HIV model with drug-resistant mutants. Appl. Math. Comput. 188, 1193–1204 (2007)
Kirschner, D., Lenhart, S., Serbin, S.: Optimal control of the chemotherapy of HIV. J. Math. Biol. 35, 775–792 (1997)
Kirschner, D.E., Webb, G.F.: Immunotherapy of HIV-1 infection. J. Biol. System 6(1), 71–83 (1998)
Tincati, C., Monforte, A., Marchetti, G.: Immunological mechanisims of interlukin-2(IL-2) treatment in HIV/AIDS diseases. Curr. Mol. Pharm. 2, 40–45 (2009)
Paoli, D.P.: Immmunological effects of interleukin-2 therapy in human immunodeficiency virus-positive subjects. Clin. Diagn. Lab. Immunol. 8(4), 671–677 (2001)
Choi, W.T., Jing, A.: Biology and clinical relevance of chemokines and chemokine receptors CXCR4 and CCR5 in human diseases. Exp. Biol. Med. 236, 637–647 (2011)
Gaertnera, H., Cerinia, F., Escolaa, J.M., Kuenzia, G., Melottia, A., Offorda, R., Rossitto-Borlata, I., Nedellecc, R., Salkowitzc, J., Gorochovd, G., Mosierc, D., Hartleya, O.: Highly potent, fully recombinant anti-HIV chemokines: reengineering a low-cost microbicide. PNAS 105(46), 17706–17711 (2008)
Banchereau, J., Palucka, A.K.: Dendritic cells as therapeutic vaccines against cancer. Nat. Rev. Immunol. 5, 296–306 (2005)
Santini, S.M., Belardelli, F.: Advances in the use of dendritic cells and new adjuvants for the development of therapeutic vaccines. Stem Cells 21, 495–505 (2003)
Lu, W., Arraes, L.C., Ferreira, W.T., Andrieu, J.M.: Therapeutic dendritic-cell vaccine for chronic HIV-1 infection. Nat. Med. 10, 1359–1365 (2004)
Gessani, S., Belardelli, F.: The Biology of Dendritic Cells and HIV Infection Sandra. Springer, (2007)
Garcia, F., Lejeune, M., Climent, N., Gil, C., Alcami, J., Morente, V., Alos, L., Ruiz, A., Setoain, J., Fumero, E., Castro, P., Lopez, A., Cruceta, A., Piera, C., Florence, E., Pereira, A., Libois, A., Gonzalez, N., Guila, M., Caballero, M., Lomena, F., Joseph, J., Miro, J.M., Pumarola, T., Plana, M., Gatell, J.M., Gallart, T.: Therapeutic immunization with dendritic cells loaded with heat-inactivated autologous HIV-1 in patients with chronic HIV-1 infection. J. Infect Dis. 191, 1680–1685 (2005)
Song, B., Lou, J., Wen, Q.: Modeling two different therapy strategies for drug T-20 on HIV-1 patients. Appl. Math. Mech. 32(4), 419–436 (2011)
Bao-dan, T., Yhang, Q.: Equilibrium and permanance for an autonomous competitive system with feedback control. Appl. Math. Sci. 50(2), 2501–2508 (2008)
Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection. Math. Biosci. 200, 44–57 (2006)
Zhou, X., Song, X., Shi, X.: A Differential equation model of HIV infection of \(CD4^+T\) cells with cure rate. J. Math. Anal. appl. 342, 1342–1355 (2008)
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Roy, P.K. (2015). Introduction. In: Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-287-852-6_1
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DOI: https://doi.org/10.1007/978-981-287-852-6_1
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