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Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell transmissions

Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell... In this paper, we analyze models of drug therapy for a HIV model with multiple delays considered in Chen et al. (J Math Anal Appl 442:642–672, 2016). As expected, in the presence of perfect inhibitors the populations of infected cells, virus, and effector cells decay exponentially to zero. When protease inhibitors are used, the production of infectious virions is diminished, as shown in our drug therapy model. First, we prove that the solution is positive and bounded from above. Our main result states that both the infected cell and infectious virus populations are asymptotically bounded by terms proportional to $$1-\eta $$ 1 - η , where $$\eta \in [0,1]$$ η ∈ [ 0 , 1 ] represents the protease inhibitor(s) effectiveness. Furthermore, under an additional condition, the infectious virus population is asymptotically bounded by a constant multiple of $$(1-\eta )^2$$ ( 1 - η ) 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Mathematics and Computing Springer Journals

Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell transmissions

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Korean Society for Computational and Applied Mathematics
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theory of Computation; Mathematics of Computing
ISSN
1598-5865
eISSN
1865-2085
DOI
10.1007/s12190-018-1196-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we analyze models of drug therapy for a HIV model with multiple delays considered in Chen et al. (J Math Anal Appl 442:642–672, 2016). As expected, in the presence of perfect inhibitors the populations of infected cells, virus, and effector cells decay exponentially to zero. When protease inhibitors are used, the production of infectious virions is diminished, as shown in our drug therapy model. First, we prove that the solution is positive and bounded from above. Our main result states that both the infected cell and infectious virus populations are asymptotically bounded by terms proportional to $$1-\eta $$ 1 - η , where $$\eta \in [0,1]$$ η ∈ [ 0 , 1 ] represents the protease inhibitor(s) effectiveness. Furthermore, under an additional condition, the infectious virus population is asymptotically bounded by a constant multiple of $$(1-\eta )^2$$ ( 1 - η ) 2 .

Journal

Journal of Applied Mathematics and Computing – Springer Journals

Published: Jun 4, 2018

References

  • Application of the decomposition method to the understanding of HIV immune dynamics
    Adjedj, B
  • Periodic oscillations in leukopoiesis models with two delays
    Adimy, M; Crauste, F; Ruan, S
  • A parameter sensitivity methodology in the context of HIV delay equation models
    Banks, HT; Bortz, DM
  • A 3(2) pair of Runge–Kutta formulas
    Bogacki, P; Shampine, LF
  • HIV-1 infection and low steady state viral loads
    Callaway, DS; Perelson, AS
  • Stability analysis in delayed within-host viral dynamics with both viral and cellular infections
    Chen, S-S; Cheng, C-Y; Takeuchi, Y
  • Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model
    Chen, X; Cao, J; Park, JH; Qiu, J
  • Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models
    Ciupe, MS; Bivort, BL; Bortz, DM
  • A delay-differential equation model of HIV infection of CD4+ T-cells
    Culshaw, RV; Ruan, S
  • Dynamics of HIV variants and specific cytotoxic T-cell recognition in nonprogressors and progressors
    Haas, G; Hosmalin, A; Hadida, F; Duntze, J; Debré, P; Autran, B
  • A retarded Gronwall-like inequality and its applications
    Lipovan, O
  • Global dynamics of an in-host viral model with intracellular delay
    Li, MY; Shu, H
  • Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy
    Liu, S; Wang, L
  • Optimal control of chemotherapy of HIV model using the coupled Adomian/Alienor methods
    Manseur, S; Attalah, K; Cherruault, Y
  • Parameter identification of an HIV model by the combined Adomian/Alienor method
    Manseur, S; Messaoudi, N; Cherruault, Y
  • Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays
    Monica, C; Pitchaimani, M
  • Population dynamics of immune responses to persistent viruses
    Nowak, MA; Bangham, CR
  • A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data
    Pawelek, KA; Liu, S; Pahlevani, F; Rong, L
  • Modelling viral and immune system dynamics
    Perelson, AS
  • Mathematical analysis of HIV-1 dynamics in vivo
    Perelson, AS; Nelson, PW
  • Solving DDEs in MATLAB
    Shampine, LF; Thompson, S
  • Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay
    Zhu, H; Zou, X