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Introduction

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Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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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

  1. Nowak, M.A., May, R.M.: AIDS pathogenesis: mathematical models of HIV and SIV infections. AIDS 7, S3–S18 (1993)

    Article  Google Scholar 

  2. Bonhoeffer, S., Coffin, J.M., Nowak, M.A.: Human immunodeficiency virus drug therapy and virus load. J. Virol. 71, 3275–3278 (1997)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. Layne, S.P., Spouge, J.L., Dembo, M.: Quantifying the infectivity of human immunodeficiency virus. Proc. Nat. Acad. Sci. USA 86, 4644 (1989)

    Article  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Murray, J.M., Kaufmann, A.D., Kelleher, D.A.: A model of primary HIV infection. Math. Biosc. 154, 57–85 (1998)

    Article  MATH  Google Scholar 

  7. Nowak, MA., May, R.M.: Virus Dynamics, Cambridge University Press, Cambridge, UK.112 (2000)

    Google Scholar 

  8. Perelson, A.S., Krischner, D.E., De-Boer, R.: Dynamics of HIV infection of CD4 T cells. Math. Biosc. 114, 81–125 (1993)

    Article  MATH  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. Lobritz, M.A., Ratcliff, A.N., Arts, E.J.: HIV-1 entry, inhibitors, and resistance. Viruses 2, 1069–1105 (2010)

    Article  Google Scholar 

  11. Robert, W., Trono, D.: The plasma membrane as a combat zone in the HIV battlefield. Genes Dev 14, 2677–2688 (2000)

    Article  Google Scholar 

  12. Xiao, D., Bossert, W.H.: An intra-host mathematical model on interaction between HIV and malaria. Bull. Math. Biol. 72, 1892–1911 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Banchereau, J., Steinman, R.M.: Dendritic cells and the control of immunity. Nature 392, 245–252 (1998)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Townsend, A., Bodmer, H.: Antigen recognition by class Irestricted T lymphocytes. Annu. Rev. Immunol. 7, 601–624 (1989)

    Article  Google Scholar 

  18. York, I., Rock, K.: Antigen processing and presentation by the class I major histocompatibility complex. Annu. Rev. Immunol. 14, 369–396 (1996)

    Article  Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. Weiss, A., Littman, D.: Signal transduction by lymphocyte antigen receptors. Cell 76, 263–274 (1994)

    Article  Google Scholar 

  21. Wange, R., Samelson, L.: Complex complexes: signaling at the TCR. Immunity 5, 197–205 (1996)

    Article  Google Scholar 

  22. Berke, G.: The CTL’s kiss of death. Cell 81, 9–12 (1995)

    Article  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. Tschopp, J., Hofmann, K.: Cytotoxic T cells: more weapons for new targets? Trends Microbiol. 4, 91–94 (1996)

    Article  Google Scholar 

  25. Culshaw, R.V., Ruan, S.: A delay-differentianal equation model of HIV infection of CD4\(^{+}\)T-cells. Math. Biosci. 165, 425–444 (2000)

    Article  Google Scholar 

  26. 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)

    Article  MathSciNet  Google Scholar 

  27. Coffin, J.M.: HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy. Sci. 267, 482–489 (1995)

    Article  Google Scholar 

  28. Callaway, D.S., Perelson, A.S.: HIV-1 infection and low virul loads. Bull. Math. Biol. 64, 29–64 (2002)

    Article  MATH  Google Scholar 

  29. Culshaw, R.V., Rawn, S., Spiteri, R.J.: Optimal HIV treatment by maximising immuno response. J. Math. Biol. 48, 545–562 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Zurakowski, R., Teel, A.R.: A model predictive control based scheduling method for HIV therapy. J. Theor. Biol. 238, 368–382 (2006)

    Article  MathSciNet  Google Scholar 

  31. Kirschner, D.E., Webb, G.F.: A model of treatment strategy in the chemotherapy of AIDS. Bull. Math. Biol. 58, 167–190 (1996)

    Article  MATH  Google Scholar 

  32. Perelson, A.S., Nelson, P.W.: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Theor. 41, 3–41 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. 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)

    Google Scholar 

  35. 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)

    Article  Google Scholar 

  36. 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)

    Google Scholar 

  37. 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)

    Article  MathSciNet  MATH  Google Scholar 

  38. 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)

    Article  MathSciNet  Google Scholar 

  39. Kwon, H.D.: Optimal treatment strategies derived from a HIV model with drug-resistant mutants. Appl. Math. Comput. 188, 1193–1204 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  40. Kirschner, D., Lenhart, S., Serbin, S.: Optimal control of the chemotherapy of HIV. J. Math. Biol. 35, 775–792 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  41. Kirschner, D.E., Webb, G.F.: Immunotherapy of HIV-1 infection. J. Biol. System 6(1), 71–83 (1998)

    Article  MATH  Google Scholar 

  42. 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)

    Article  Google Scholar 

  43. Paoli, D.P.: Immmunological effects of interleukin-2 therapy in human immunodeficiency virus-positive subjects. Clin. Diagn. Lab. Immunol. 8(4), 671–677 (2001)

    Google Scholar 

  44. 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)

    Article  Google Scholar 

  45. 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)

    Article  Google Scholar 

  46. Banchereau, J., Palucka, A.K.: Dendritic cells as therapeutic vaccines against cancer. Nat. Rev. Immunol. 5, 296–306 (2005)

    Article  Google Scholar 

  47. 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)

    Article  Google Scholar 

  48. 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)

    Article  Google Scholar 

  49. Gessani, S., Belardelli, F.: The Biology of Dendritic Cells and HIV Infection Sandra. Springer, (2007)

    Google Scholar 

  50. 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)

    Article  Google Scholar 

  51. 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)

    Article  MathSciNet  MATH  Google Scholar 

  52. Bao-dan, T., Yhang, Q.: Equilibrium and permanance for an autonomous competitive system with feedback control. Appl. Math. Sci. 50(2), 2501–2508 (2008)

    Google Scholar 

  53. Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection. Math. Biosci. 200, 44–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  54. 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)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Department of Mathematics, Jadavpur University, Kolkata, India

    Priti Kumar Roy

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  1. Priti Kumar Roy
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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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