Stability Analysis of Two Mathematical Models of Dynamics of CTLS in the Antiretroviral Therapy for HIV Infection, By Painleve Property Analysis
DOI:
https://doi.org/10.26821/IJSRC.12.3.2024.120302Keywords:
Cytotoxic T Lymphocyte, Antiretroviral Therapy, Painleve Property, Dynamics, CD4+ T cell, Parameters, Virus, Leukocyte, Lymphocyte, immunodeficiency, Infection, Cytokines, Resonances, StabilityAbstract
It is confirmed that Cytotoxic T-Lymphocyte (CTL) play crucial role in the controlling of proliferation of HIV virus in a HIV infected patient.. In search of possible steady states of viral load and CD4+T cells density, few mathematical models of dynamics of CTLs during antiretroviral therapy of HIV infection are reported recently. Stability analysis of two of these mathematical models of dynamics of CTLs are studied using Painleve property analysis (PPA) method. Their results are compared with clinical data and PPA that of another standard model of dynamics of CD4+ T cells and justified the results.
References
P.K.Roy,in “ Mathematical Model for Therapeutic Approaches to Control HIV disease Transmission”, Springer-Verlg, Singapore (2015).
. H.C.Lane and A.S. Faucci, in “ Modern Concepts and Therapeutic Challenges “ ed. A.S.Boarder, Marcel Decker pub. New York, 1987, pp.185.
.M.A.Nowak and R.M.May,in “Virus Dynamics”, Cambridge University Press,Cambridge,UK. pp 112, (2000).
. P.K.Roy and A.N.Chatterjee, in “Lecture Notes in Engineering and Computer Science”, pp 615, (2010).
S.Merril, in “ Mathematical and Statidtical Approaches to AIDS Epidemology” Lecture Notes in Bio-Math. 83, Springer-Verlag,New York (1989).
. Y.Linand and B.A.Askonas, J.Exp.Med.,154, pp225 (1981).
. J.A.Byrne and M.B.A.Oldstone, J.Virol.51,pp682 (1984).
. M.B.A.Oldstone,J.Nature,321,pp239 (1986).
. M.A.Nowak and R.M.May,J.AIDS,07, S3 (1993).
. S.Bonhoeffer, J.M.Coffin and M.A.Nowak, J.Virol, 71, pp3275 (1997)
. S.A.Kalumas,P.J.Goulder,A.K.Shea, A.K.Jones,N.G.Trocha,G.S.Ogg and B.D.Walke, J.Virol. 73, pp6721 (1999).
. A.S.Pereleson,A.U.Neumann,J.M.Markowitz,M.Leonard and R.Thiebeut, J.Annals of Appl.Statistics,01,pp1593 (2017).
. M.A.Nowak and C.R.M.Bengham, J.Science, 272 ,pp 74 (1996)
.D.D.Ho, A.U.Neumann, A.S.Pereleson ,W.Chen,M.Leonard,and J.M.Markowitz. Jr.Nature, vol.373, pp.123-126 ,1995.
. A.S.Pereleson,A.U.Neumann,J.M.Markowitz,M.Leonard and Ho.D.D. ,Jr.Science, vol.271, pp.1582,(1996).
. R.Thiebeut, J.Drylawicz,M.Prague, C.Lacabratz, S.Beq, Anna Jarne, T.Craughs,R.Sekely, M.M.Lederman and J.Sereti. Jr,Plos.Comput.Biol. 10E1003630, (2014).
. Anna Jarne, C.D.Daniel, V.Laura, P.Melanic, Yeves Levy and R.Thiebeut, Jr.Annals of Appl.Statistics, vol. 01,pp.159 ( 2017).
. M.A.Lobinitz, A.N.Ratcliff and E.J.Arts,J.Viruses,02,pp1069 (2019).
. A.K.Seucell,D.A.Price,A.Oxenius,A.D.Kelleher and R.E.Phillips, J.Stem Cell, 18,pp 233 (2000).
. J.Tschopp and K.Hoffmann, J.Trends in Microbiol.,04,pp9 (1996).
. J.M.Coffin, J,Sci.267,pp482 (1995).
. R.V.Culshaw and S.Ruan, J.Math.Biosci. 65,pp425 (2000).
. J.M.Coffin,J.SCi.267,pp482 (1995).
. D.S.Callawey and A.S.Pereleson,J.Bull.Math.Biol.64, 64,pp29(2002).
.A.S.Pereleson, and P.W.Nelson, J.SIAM Theor.,41,pp03 (1999).
. R.V.Culshaw,S.Rawn and R.J.Spitri, J.Math.Biol. 48, pp545 (2004).
. B.V.Baby,J.IJSRC,11,58,(2023),DOI. 10.26821/IJSRC.11.1.2023.110109.
. A.Ramani,B.Grammaticos and T.Bountis, Jr.Physics Reports, vol. 180, pp.159, (1989).
. E.L.Ince, in “Ordinary Differential Equations” ,pub.Dover ,pp 346,(1926).
. M.Weiss, M.Tabor, and G.Carnevale, J.Math.Phys., 21, pp.522 (1980).
. N.Nirmala,M.J.Vedan and B.V.Baby, J.Math.Phys., 27, pp.2640, (1986).
. N.nirmala, M.J.Vedan and B.V.Baby,J.Math.Phys., 27, pp. 2644 ,(1986).
. V.Rai, S.Konar, and B.V.Baby, J.Phys.Letts., 183A , pp.76, (1993).
. A.S.Perelson, D.E.Krischner and R. De Boer, J.Math.Bio.Sci.,114, pp81 (1993).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 B.V.Baby
This work is licensed under a Creative Commons Attribution 4.0 International License.
