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Journal of Applied Mathematics and Computing

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07.12.2016 | Original Research

Analyzing on stability of HIV-PI model with general incidence rate

verfasst von: M. Divya, M. Pitchaimani

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

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Abstract

In this article, we have constructed a PI model with general incidence rate and humoral immunity. We have analyzed about the equilibrium points in general case. Using appropriate Lyapunov functional and Lasalle’s invariance principle, the global stability of the newly constructed model have been discussed. Using patient data we have discussed about the model numerically.

Vorheriger Artikel Stability of impulsive delay differential equations

Nächster Artikel On a fractional higher order initial value problem

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Fauci, A.S.: HIV and AIDS: 20 years of science. Nat. Med. 9, 839–843 (2003)CrossRef

Anderson, R.M., Gupta, S., May, R.M.: Potential of community—wide chemotherapy or immunotherapy to control the spread of HIV-1. Nat. Lond. 350, 356–359 (1991)CrossRef

Anderson, R.M., May, R.M., Mclean, A.R.: Possible demographic consequences of AIDS in developing countries. Nature 332, 228–234 (1988)CrossRef

Blower, S.M.: Behavior changes and stabilization of seroprevalence levels, correlation or causation. JAIDS 4, 920–923 (1991)

Blower, S.M., Hartel, D., Dowlatabadi, H., Anderson, R.M., May, R.M.: Sex, drugs & HIV: a mathematical model for New York City. Philos. Trans. R. Soc. Lond. B 331, 171–187 (1991)CrossRef

Dietz, K., Hadeler, K.P.: Epidemiology models for sexually transmitted diseases. J. Math. Biol. 26, 1–25 (1988)MathSciNetCrossRefMATH

Jacquez, J.A., Simon, C.P., Koopman, J., Sattenspiel, L., Perry, T.: Modelling and analysis HIV transmission: the effect of contact patterns. Math. Biosci. 92, 119–199 (1988)MathSciNetCrossRefMATH

Koopman, J., Simon, C., Jacquez, J., et al.: Sexual partner selectiveness effects on homosexual HIV transmission dynamics. JAIDS 1, 486–504 (1988)

Le Pont, F., Blower, S.M.: The supply & demand dynamics of sexual behavior: implications for a heterosexual HIV epidemic. JAIDS 4, 987–999 (1991)

10.

May, R.M., Anderson, R.M., Blower, S.M.: The epidemiology and transmission dynamics of HIV/AIDS. Daedalus 118(2), 163–201 (1989)

11.

Blower, S.M., Medley, G.F.: Epidemiology, HIV & drugs: Mathematical models & data. Br. J. Addict. 87, 31–39 (1992)CrossRef

12.

Ray, M., Logan, R., Sterne, J.A., HIV-CAUSAL Collaboration et al.: The effect of combined antiretroviral therapy on the overall mortality of HIV-infected individuals. AIDS 24, 123–137 (2010)

13.

Nakagawa, F., Lodwick, R.K., Smith, C.J., et al.: Projected life expectancy of people with HIV according to timing of diagnosis. AIDS 26, 335–343 (2012)CrossRef

14.

Archin, N.M., Vaidya, N.K., Kuruc, J.D., et al.: Immediate antiviral therapy appears to restrict resting CD4+ cell HIV-1 infection without accelerating the decay of latent infection. Proc. Natl. Acad. Sci. USA 109, 9523–9528 (2012)CrossRef

15.

Taiwo, B., Matining, R.M., Zheng, L., et al.: Associations of T cell activation and infl ammatory biomarkers with virological response to darunavir/ritonavir plus raltegravir therapy. J. Antimicrob. Chemother. 68, 1857–1861 (2013)CrossRef

16.

Janeway, C., Travers, P., Walport, M., Shlomchik, M.: Immunobiology: The Immune System in Health and Diseases. Garland Science, London (2006)

17.

Carpenter, C.: Universal access to antiretroviral therapy: when, not if. Clin. Infect. Dis. 42, 260–261 (2006)CrossRef

18.

Calmy, A., Petoumenos, K., Lewden, C., Law, M., Bocquentin, F., Hesse, K., Cooper, D., Carr, A., Bonnet, F.: Combination antiretroviral therapy without a nucleoside reverse transcriptase inhibitor: experience from 334 patients in three cohorts. HIV Med. 8, 171–180 (2007)CrossRef

19.

Chiyaka, C., Garira, W., Dube, S.: Modelling immune response and drug therapy in human malaria infection. Comput. Math. Methods Med. 9, 143–163 (2008)MathSciNetCrossRefMATH

20.

Culshaw, R.V., Ruan, S.G., Spiteri, R.J.: Optimal HIV treatment by maximising immune response. J. Math. Biol. 48, 545–562 (2004)MathSciNetCrossRefMATH

21.

Ji, Y., Min, L.Q., Zheng, Y., Su, Y.M.: A viral infection model with periodic immune response and nonlinear CTL response. Math. Comput. Simul. 80, 2309–2316 (2010)MathSciNetCrossRefMATH

22.

Li, M.Y., Shu, H.Y.: Global dynamics of a mathematical model for HTLV-1 infection of CD4+T cells with delayed CTL response. Nonlinear Anal. Real World Appl. 13, 1080–1092 (2012)MathSciNetCrossRefMATH

23.

Song, X.Y., Wang, S.L., Dong, J.: Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune response. J. Math. Anal. Appl. 373, 345–355 (2011)MathSciNetCrossRefMATH

24.

Wang, S.L., Song, X.Y., Ge, Z.H.: Dynamics analysis of a delayed viral infection model with immune impairment. Appl. Math. Model. 35, 4877–4885 (2011)MathSciNetCrossRefMATH

25.

Wang, K.F., Wang, W.D., Liu, X.N.: Global stability in a viral infection model with lytic and nonlytic immune responses. Comput. Math. Appl. 51, 1593–1610 (2006)MathSciNetCrossRefMATH

26.

Xie, Q.Z., Huang, D.W., Zhang, S.D., Cao, J.: Analysis of a viral infection model with delayed immune response. Appl. Math. Model. 34, 2388–2395 (2010)MathSciNetCrossRefMATH

27.

Nakata, Y.: Global dynamics of a cell mediated immunity in viral infection models with distributed delays. J. Math. Anal. Appl. 375, 14–27 (2011)MathSciNetCrossRefMATH

28.

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, 98–109 (2012)MathSciNetCrossRefMATH

29.

Wang, S.F., Zou, D.Y.: Global stability of in-host viral models with humoral immunity and intracellular delays. Appl. Math. Model. 36, 1313–1322 (2012)MathSciNetCrossRefMATH

30.

Wang, Z.P., Xu, R.: Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response. Commun. Nonlinear Sci. Numer. Simul. 17, 964–978 (2012)MathSciNetCrossRefMATH

31.

Yous, N., Hattaf, K., Tridane, A.: Modeling the adaptive immune response in HBV infection. J. Math. Biol. 63, 933–957 (2011)MathSciNetCrossRefMATH

32.

Zhu, H.Y., Luo, Y., Chen, M.L.: Stability and Hopf bifurcation of a HIV infection model with CTL-response delay. Comput. Math. Appl. 62, 3091–3102 (2011)MathSciNetCrossRefMATH

33.

Zhu, H.Y., Zou, X.F.: Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discret. Contin. Dyn. Syst. B 12, 511–524 (2009)MathSciNetCrossRefMATH

34.

Deans, J.A., Cohen, S.: Immunology of malaria. Annu. Rev. Microbiol. 37, 25–50 (1983)CrossRef

35.

Hattaf, K., Lashari, A.A., Louartassi, Y., Yousfi, n: A delayed SIR epidemic model with general incidence rate. Electron. J. Qual. Theory Differ. Equ. 3, 1–9 (2013)MathSciNetCrossRefMATH

36.

Ouifki, R., Witten, G.: Stability analysis of a model for HIV infection with RTI and three intracellular delays. BioSystems 95, 16 (2009)CrossRef

37.

Yang, X., Chen, L., Chen, J.: Permanance and positive periodic solution for the single species non autonomous delay diffusion models. Comput. Math. Appl. 32, 109–116 (1996)MathSciNetCrossRef

38.

LaSalle, J.P.: The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA, USA (1976)

Titel: Analyzing on stability of HIV-PI model with general incidence rate
verfasst von: M. Divya
M. Pitchaimani
Publikationsdatum: 07.12.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-1073-0

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