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2017 | OriginalPaper | Chapter

Effects of Delay and Drug on HIV Infection

Author : Saroj Kumar Sahani

Published in: Proceedings of Sixth International Conference on Soft Computing for Problem Solving

Publisher: Springer Singapore

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Abstract

This article discusses delayed model of HIV infection with combination therapy consisting of RTI and PI drug. The delay included in this article two kinds of delays viz. immune response delay and intracellular delay. A well known growth law so called logistic growth is assumed for uninfected and healthy T cell. Local properties of the infection free equilibrium point is discussed in terms of \(R_0\), the basic reproduction number. The existence of Hopf bifurcation with respect to delayed parameter is verified using geometric switching conditions numerically because of delay dependent parameters in the model. Extensive numerical simulations have been carried out on the model to ascertain the effects of drug on viral dynamic and disease progression.

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Literature
1.
go back to reference Allen, L.J., Brauer, F., Van den Driessche, P., Wu, J.: Mathematical Epidemiology. Springer, Heidelberg (2008) Allen, L.J., Brauer, F., Van den Driessche, P., Wu, J.: Mathematical Epidemiology. Springer, Heidelberg (2008)
2.
go back to reference Andersen, R.M., May, R.M.: Epidemiological parameters of HIV transmission. Nature 333(6173), 514–519 (1988)CrossRef Andersen, R.M., May, R.M.: Epidemiological parameters of HIV transmission. Nature 333(6173), 514–519 (1988)CrossRef
3.
go back to reference Anderson, R.M.: Mathematical and statistical studies of the epidemiology of HIV. AIDS 3(6), 333–346 (1989)CrossRef Anderson, R.M.: Mathematical and statistical studies of the epidemiology of HIV. AIDS 3(6), 333–346 (1989)CrossRef
4.
go back to reference Bachar, M., Dorfmayr, A.: HIV treatment models with time delay. C.R. Biol. 327(11), 983–994 (2004)CrossRef Bachar, M., Dorfmayr, A.: HIV treatment models with time delay. C.R. Biol. 327(11), 983–994 (2004)CrossRef
5.
go back to reference Bailey, J.J., Fletcher, J.E., Chuck, E.T., Shrager, R.I.: A kinetic model of CD4+ lymphocytes with the human immunodeficiency virus (HIV). BioSystems 26(3), 177–183 (1992)CrossRef Bailey, J.J., Fletcher, J.E., Chuck, E.T., Shrager, R.I.: A kinetic model of CD4+ lymphocytes with the human immunodeficiency virus (HIV). BioSystems 26(3), 177–183 (1992)CrossRef
6.
go back to reference Bairagi, N., Adak, D.: Global analysis of HIV-1 dynamics with hill type infection rate and intracellular delay. Appl. Math. Model. 38(21), 5047–5066 (2014)MathSciNetCrossRef Bairagi, N., Adak, D.: Global analysis of HIV-1 dynamics with hill type infection rate and intracellular delay. Appl. Math. Model. 38(21), 5047–5066 (2014)MathSciNetCrossRef
7.
go back to reference Banks, H., Bortz, D.: A parameter sensitivity methodology in the context of HIV delay equation models. J. Math. Biol. 50(6), 607–625 (2005)MathSciNetCrossRefMATH Banks, H., Bortz, D.: A parameter sensitivity methodology in the context of HIV delay equation models. J. Math. Biol. 50(6), 607–625 (2005)MathSciNetCrossRefMATH
8.
go back to reference Banks, H., Bortz, D., Holte, S.: Incorporation of variability into the modeling of viral delays in HIV infection dynamics. Math. Biosci. 183(1), 63–91 (2003)MathSciNetCrossRefMATH Banks, H., Bortz, D., Holte, S.: Incorporation of variability into the modeling of viral delays in HIV infection dynamics. Math. Biosci. 183(1), 63–91 (2003)MathSciNetCrossRefMATH
9.
go back to reference Beretta, E., Kuang, Y.: Modeling and analysis of a marine bacteriophage infection with latency period. Nonlinear Anal. Real World Appl. 2(1), 35–74 (2001)MathSciNetCrossRefMATH Beretta, E., Kuang, Y.: Modeling and analysis of a marine bacteriophage infection with latency period. Nonlinear Anal. Real World Appl. 2(1), 35–74 (2001)MathSciNetCrossRefMATH
10.
go back to reference Beretta, E., Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay-dependent parameters. SIAM J. Math. Anal. 33(31), 144–1165 (2002)MathSciNetMATH Beretta, E., Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay-dependent parameters. SIAM J. Math. Anal. 33(31), 144–1165 (2002)MathSciNetMATH
11.
go back to reference Bonhoeffer, S., May, R.M., Shaw, G.M., Nowak, M.A.: Virus dynamics and drug therapy. Proc. Nat. Acad. Sci. 94(13), 6971–6976 (1997)CrossRef Bonhoeffer, S., May, R.M., Shaw, G.M., Nowak, M.A.: Virus dynamics and drug therapy. Proc. Nat. Acad. Sci. 94(13), 6971–6976 (1997)CrossRef
12.
go back to reference Brauer, F., Castillo-Chavez, C., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology, vol. 1. Springer, New York (2001)CrossRefMATH Brauer, F., Castillo-Chavez, C., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology, vol. 1. Springer, New York (2001)CrossRefMATH
13.
go back to reference Chiyaka, C., Garira, W., Dube, S.: Modelling immune response and drug therapy in human malaria infection. Comput. Math. Methods Med. 9(2), 143–163 (2008)MathSciNetCrossRefMATH Chiyaka, C., Garira, W., Dube, S.: Modelling immune response and drug therapy in human malaria infection. Comput. Math. Methods Med. 9(2), 143–163 (2008)MathSciNetCrossRefMATH
14.
go back to reference Culshaw, R.V., Ruan, S.: A delay-differential equation model of HIV infection of CD4\(^+\) T-cells. Math. Biosci. 165(1), 27–39 (2000)CrossRefMATH Culshaw, R.V., Ruan, S.: A delay-differential equation model of HIV infection of CD4\(^+\) T-cells. Math. Biosci. 165(1), 27–39 (2000)CrossRefMATH
15.
go back to reference Culshaw, R.V., Ruan, S., Webb, G.: A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46(5), 425–444 (2003)MathSciNetCrossRefMATH Culshaw, R.V., Ruan, S., Webb, G.: A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46(5), 425–444 (2003)MathSciNetCrossRefMATH
16.
go back to reference Deans, J.A., Cohen, S.: Immunology of malaria. Annu. Rev. Microbiol. 37(1), 25–50 (1983)CrossRef Deans, J.A., Cohen, S.: Immunology of malaria. Annu. Rev. Microbiol. 37(1), 25–50 (1983)CrossRef
17.
go back to reference Dixit, N.M., Markowitz, M., Ho, D.D., Perelson, A.S.: Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy. Antivir. Ther. 9, 237–246 (2004) Dixit, N.M., Markowitz, M., Ho, D.D., Perelson, A.S.: Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy. Antivir. Ther. 9, 237–246 (2004)
18.
go back to reference Granich, R.M., Gilks, C.F., Dye, C., De Cock, K.M., Williams, B.G.: Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 373(9657), 48–57 (2009)CrossRef Granich, R.M., Gilks, C.F., Dye, C., De Cock, K.M., Williams, B.G.: Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 373(9657), 48–57 (2009)CrossRef
19.
go back to reference Grossman, Z., Polis, M., Feinberg, M.B., Grossman, Z., Levi, I., Jankelevich, S., Yarchoan, R., Boon, J., de Wolf, F., Lange, J.M., et al.: Ongoing HIV dissemination during haart. Nat. Med. 5(10), 1099–1104 (1999)CrossRef Grossman, Z., Polis, M., Feinberg, M.B., Grossman, Z., Levi, I., Jankelevich, S., Yarchoan, R., Boon, J., de Wolf, F., Lange, J.M., et al.: Ongoing HIV dissemination during haart. Nat. Med. 5(10), 1099–1104 (1999)CrossRef
21.
go back to reference Haynes, B.F., Gilbert, P.B., McElrath, M.J., Zolla-Pazner, S., Tomaras, G.D., Alam, S.M., Evans, D.T., Montefiori, D.C., Karnasuta, C., Sutthent, R., et al.: Immune-correlates analysis of an HIV-1 vaccine efficacy trial. N. Engl. J. Med. 366(14), 1275–1286 (2012)CrossRef Haynes, B.F., Gilbert, P.B., McElrath, M.J., Zolla-Pazner, S., Tomaras, G.D., Alam, S.M., Evans, D.T., Montefiori, D.C., Karnasuta, C., Sutthent, R., et al.: Immune-correlates analysis of an HIV-1 vaccine efficacy trial. N. Engl. J. Med. 366(14), 1275–1286 (2012)CrossRef
22.
go back to reference Herz, A., Bonhoeffer, S., Anderson, R.M., May, R.M., Nowak, M.A.: Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. Proc. Nat. Acad. Sci. 93(14), 7247–7251 (1996)CrossRef Herz, A., Bonhoeffer, S., Anderson, R.M., May, R.M., Nowak, M.A.: Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. Proc. Nat. Acad. Sci. 93(14), 7247–7251 (1996)CrossRef
24.
go back to reference Ho, D.D.: Toward HIV eradication or remission: the tasks ahead. Science 280(5371), 1866–1867 (1998)CrossRef Ho, D.D.: Toward HIV eradication or remission: the tasks ahead. Science 280(5371), 1866–1867 (1998)CrossRef
25.
go back to reference Ho, D.D., Neumann, A.U., Perelson, A.S., Chen, W., Leonard, J.M., Markowitz, M., et al.: Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 373(6510), 123–126 (1995)CrossRef Ho, D.D., Neumann, A.U., Perelson, A.S., Chen, W., Leonard, J.M., Markowitz, M., et al.: Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 373(6510), 123–126 (1995)CrossRef
26.
go back to reference Holder, B.P., Beauchemin, C.A.: Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture. BMC Public Health 11(Suppl 1), S10 (2011)CrossRef Holder, B.P., Beauchemin, C.A.: Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture. BMC Public Health 11(Suppl 1), S10 (2011)CrossRef
27.
go back to reference Hraba, T., Doležal, J., čelikovský, S.: Model-based analysis of CD4+ lymphocyte dynamics in HIV infected individuals. Immunobiology 181(1), 108–118 (1990)CrossRef Hraba, T., Doležal, J., čelikovský, S.: Model-based analysis of CD4+ lymphocyte dynamics in HIV infected individuals. Immunobiology 181(1), 108–118 (1990)CrossRef
28.
go back to reference Jiang, X., Zhou, X., Shi, X., Song, X.: Analysis of stability and hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells. Chaos, Solitons Fractals 38(2), 447–460 (2008)MathSciNetCrossRefMATH Jiang, X., Zhou, X., Shi, X., Song, X.: Analysis of stability and hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells. Chaos, Solitons Fractals 38(2), 447–460 (2008)MathSciNetCrossRefMATH
29.
go back to reference Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. Lond. A: Math. Phys. Eng. Sci. 115, 700–721 (1927). The Royal SocietyCrossRefMATH Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. Lond. A: Math. Phys. Eng. Sci. 115, 700–721 (1927). The Royal SocietyCrossRefMATH
30.
go back to reference Kirschner, D.: Using mathematics to understand HIV immune dynamics. AMS Not. 43(2), 191–202 (1996)MathSciNetMATH Kirschner, D.: Using mathematics to understand HIV immune dynamics. AMS Not. 43(2), 191–202 (1996)MathSciNetMATH
31.
go back to reference Kirschner, D.E., Webb, G.F.: A mathematical model of combined drug therapy of HIV infection. Comput. Math. Methods Med. 1(1), 25–34 (1997)MATH Kirschner, D.E., Webb, G.F.: A mathematical model of combined drug therapy of HIV infection. Comput. Math. Methods Med. 1(1), 25–34 (1997)MATH
32.
go back to reference Kuang, Y.: Delay Differential Equations: With Applications in Population Dynamics. Academic Press, Boston (1993)MATH Kuang, Y.: Delay Differential Equations: With Applications in Population Dynamics. Academic Press, Boston (1993)MATH
33.
go back to reference Law, M.G., Prestage, G., Grulich, A., Van de Ven, P., Kippax, S.: Modelling the effect of combination antiretroviral treatments on HIV incidence. AIDS 15(10), 1287–1294 (2001)CrossRef Law, M.G., Prestage, G., Grulich, A., Van de Ven, P., Kippax, S.: Modelling the effect of combination antiretroviral treatments on HIV incidence. AIDS 15(10), 1287–1294 (2001)CrossRef
34.
35.
go back to reference Li, M.Y., Shu, H.: Impact of intracellular delays and target-cell dynamics on in vivo viral infections. SIAM J. Appl. Math. 70(7), 2434–2448 (2010)MathSciNetCrossRefMATH Li, M.Y., Shu, H.: Impact of intracellular delays and target-cell dynamics on in vivo viral infections. SIAM J. Appl. Math. 70(7), 2434–2448 (2010)MathSciNetCrossRefMATH
36.
go back to reference Liu, S., Wang, L.: Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Math. Biosci. Eng. 7(3), 675–685 (2010)MathSciNetCrossRefMATH Liu, S., Wang, L.: Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Math. Biosci. Eng. 7(3), 675–685 (2010)MathSciNetCrossRefMATH
37.
go back to reference Merrill, S.J.: Modeling the interaction of HIV with cells of the immune system. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, vol. 83, pp. 371–385. Springer, Heidelberg (1989)CrossRef Merrill, S.J.: Modeling the interaction of HIV with cells of the immune system. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, vol. 83, pp. 371–385. Springer, Heidelberg (1989)CrossRef
38.
go back to reference Mittler, J.E., Markowitz, M., Ho, D.D., Perelson, A.S.: Improved estimates for HIV-1 clearance rate and intracellular delay. AIDS 13(11), 1415 (1999)CrossRef Mittler, J.E., Markowitz, M., Ho, D.D., Perelson, A.S.: Improved estimates for HIV-1 clearance rate and intracellular delay. AIDS 13(11), 1415 (1999)CrossRef
39.
go back to reference Mittler, J.E., Sulzer, B., Neumann, A.U., Perelson, A.S.: Influence of delayed viral production on viral dynamics in HIV-1 infected patients. Math. Biosci. 152(2), 143–163 (1998)CrossRefMATH Mittler, J.E., Sulzer, B., Neumann, A.U., Perelson, A.S.: Influence of delayed viral production on viral dynamics in HIV-1 infected patients. Math. Biosci. 152(2), 143–163 (1998)CrossRefMATH
40.
go back to reference Murray, J.M., Emery, S., Kelleher, A.D., Law, M., Chen, J., Hazuda, D.J., Nguyen, B.Y.T., Teppler, H., Cooper, D.A.: Antiretroviral therapy with the integrase inhibitor raltegravir alters decay kinetics of HIV, significantly reducing the second phase. AIDS 21(17), 2315–2321 (2007)CrossRef Murray, J.M., Emery, S., Kelleher, A.D., Law, M., Chen, J., Hazuda, D.J., Nguyen, B.Y.T., Teppler, H., Cooper, D.A.: Antiretroviral therapy with the integrase inhibitor raltegravir alters decay kinetics of HIV, significantly reducing the second phase. AIDS 21(17), 2315–2321 (2007)CrossRef
41.
go back to reference Nelson, P.W., Mittler, J.E., Perelson, A.S.: Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters. JAIDS J. Acquir. Immune Defic. Syndr. 26(5), 405–412 (2001)CrossRef Nelson, P.W., Mittler, J.E., Perelson, A.S.: Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters. JAIDS J. Acquir. Immune Defic. Syndr. 26(5), 405–412 (2001)CrossRef
42.
go back to reference Nelson, P.W., Murray, J.D., Perelson, A.S.: A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci. 163(2), 201–215 (2000)MathSciNetCrossRefMATH Nelson, P.W., Murray, J.D., Perelson, A.S.: A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci. 163(2), 201–215 (2000)MathSciNetCrossRefMATH
43.
go back to reference Nelson, P.W., Perelson, A.S.: Mathematical analysis of delay differential equation models of HIV-1 infection. Math. Biosci. 179(1), 73–94 (2002)MathSciNetCrossRefMATH Nelson, P.W., Perelson, A.S.: Mathematical analysis of delay differential equation models of HIV-1 infection. Math. Biosci. 179(1), 73–94 (2002)MathSciNetCrossRefMATH
44.
go back to reference Nowak, M., May, R.M.: Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000)MATH Nowak, M., May, R.M.: Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000)MATH
45.
go back to reference Nowak, M.A., Bangham, C.R.: Population dynamics of immune responses to persistent viruses. Science 272(5258), 74–79 (1996)CrossRef Nowak, M.A., Bangham, C.R.: Population dynamics of immune responses to persistent viruses. Science 272(5258), 74–79 (1996)CrossRef
46.
go back to reference Nowak, M.A., May, R.M.: Virus Dynamics (2000) Nowak, M.A., May, R.M.: Virus Dynamics (2000)
47.
go back to reference Ouifki, R., Witten, G.: Stability analysis of a model for HIV infection with RTI and three intracellular delays. BioSystems 95(1), 1–6 (2009)CrossRef Ouifki, R., Witten, G.: Stability analysis of a model for HIV infection with RTI and three intracellular delays. BioSystems 95(1), 1–6 (2009)CrossRef
48.
go back to reference Pawelek, K.A., Liu, S., Pahlevani, F., Rong, L.: A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. Math. Biosci. 235(1), 98–109 (2012)MathSciNetCrossRefMATH Pawelek, K.A., Liu, S., Pahlevani, F., Rong, L.: A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. Math. Biosci. 235(1), 98–109 (2012)MathSciNetCrossRefMATH
50.
go back to reference Perelson, A.S., Kirschner, D.E., De Boer, R.: Dynamics of HIV infection of CD4\(^+\) T cells. Math. Biosci. 114(1), 81–125 (1993)CrossRefMATH Perelson, A.S., Kirschner, D.E., De Boer, R.: Dynamics of HIV infection of CD4\(^+\) T cells. Math. Biosci. 114(1), 81–125 (1993)CrossRefMATH
52.
go back to reference Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D.: HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271(5255), 1582–1586 (1996)CrossRef Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D.: HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271(5255), 1582–1586 (1996)CrossRef
53.
go back to reference Pitchaimani, M., Monica, C.: Global stability analysis of HIV-1 infection model with three time delays. J. Appl. Math. Comput. 48, 1–27 (2014)MathSciNetMATH Pitchaimani, M., Monica, C.: Global stability analysis of HIV-1 infection model with three time delays. J. Appl. Math. Comput. 48, 1–27 (2014)MathSciNetMATH
54.
go back to reference Pitchaimani, M., Monica, C., Divya, M.: Stability analysis for HIV infection delay model with protease inhibitor. Biosystems 114(2), 118–124 (2013)CrossRef Pitchaimani, M., Monica, C., Divya, M.: Stability analysis for HIV infection delay model with protease inhibitor. Biosystems 114(2), 118–124 (2013)CrossRef
55.
go back to reference Sahani, S.K.: Effects of intracellular delay and immune response delay in HIV model. Neural Parallel Sci. Comput. 23, 357–366 (2015)MathSciNet Sahani, S.K.: Effects of intracellular delay and immune response delay in HIV model. Neural Parallel Sci. Comput. 23, 357–366 (2015)MathSciNet
58.
go back to reference Sun, Z., Xu, W., Yang, X., Fang, T.: Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays. Chaos, Solitons Fractals 31(1), 39–53 (2007)MathSciNetCrossRefMATH Sun, Z., Xu, W., Yang, X., Fang, T.: Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays. Chaos, Solitons Fractals 31(1), 39–53 (2007)MathSciNetCrossRefMATH
59.
go back to reference Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection of CD4\(^+\) T cells. Math. Biosci. 200(1), 44–57 (2006)MathSciNetCrossRefMATH Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection of CD4\(^+\) T cells. Math. Biosci. 200(1), 44–57 (2006)MathSciNetCrossRefMATH
60.
go back to reference Wein, L.M., Zenios, S.A., Nowak, M.A.: Dynamic multidrug therapies for HIV: a control theoretic approach. J. Theoret. Biol. 185(1), 15–29 (1997)CrossRef Wein, L.M., Zenios, S.A., Nowak, M.A.: Dynamic multidrug therapies for HIV: a control theoretic approach. J. Theoret. Biol. 185(1), 15–29 (1997)CrossRef
61.
go back to reference Wodarz, D., Lloyd, A.L.: Immune responses and the emergence of drug-resistant virus strains in vivo. Proc. R. Soc. Lond.-B 271(1544), 1101–1110 (2004)CrossRef Wodarz, D., Lloyd, A.L.: Immune responses and the emergence of drug-resistant virus strains in vivo. Proc. R. Soc. Lond.-B 271(1544), 1101–1110 (2004)CrossRef
62.
go back to reference Wodarz, D., Nowak, M.A.: Mathematical models of HIV pathogenesis and treatment. BioEssays 24(12), 1178–1187 (2002)CrossRef Wodarz, D., Nowak, M.A.: Mathematical models of HIV pathogenesis and treatment. BioEssays 24(12), 1178–1187 (2002)CrossRef
63.
go back to reference Xiang, H., Feng, L.X., Huo, H.F.: Stability of the virus dynamics model with beddington-deangelis functional response and delays. Appl. Math. Model. 37(7), 5414–5423 (2013)MathSciNetCrossRef Xiang, H., Feng, L.X., Huo, H.F.: Stability of the virus dynamics model with beddington-deangelis functional response and delays. Appl. Math. Model. 37(7), 5414–5423 (2013)MathSciNetCrossRef
64.
go back to reference Zhu, H., Zou, X.: Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete Contin. Dyn. Syst. Ser. B 12(2), 511–524 (2009)MathSciNetCrossRefMATH Zhu, H., Zou, X.: Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete Contin. Dyn. Syst. Ser. B 12(2), 511–524 (2009)MathSciNetCrossRefMATH
Metadata
Title
Effects of Delay and Drug on HIV Infection
Author
Saroj Kumar Sahani
Copyright Year
2017
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-3325-4_38

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