IMMUNE RESPONSE IN HIV EPIDEMICS FOR DISTINCT TRANSMISSION RATES AND FOR SATURATED CTL RESPONSE

被引：14
作者：
Carvalho, Ana R. M. [1 ]
Pinto, Carla M. A. [2 ]
机构：
[1] Univ Porto, Fac Sci, Rua Campo Alegre S-N, P-4440452 Porto, Portugal
[2] Univ Porto, Ctr Math, Polytech Porto, Sch Engn, Rua Dr Antonio Bernardino de Almeida 431, P-4249015 Porto, Portugal
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2019年 / 14卷 / 03期
关键词：
HIV infection; disease transmission rates; saturated CTL response; fractional model; FRACTIONAL CALCULUS; INFECTION; MODEL; DYNAMICS; VACCINATION; IMPACT; CELLS;
D O I：
10.1051/mmnp/2019007
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we study the immune response in a fractional order model for HIV dynamics, for distinct disease transmission rates and saturated cytotoxic T-lymphocyte (CTL) response. Our goal is twofold: (i) to analyze the role of the order of the fractional derivative, alpha, on the efficacy of the immune response, (ii) to examine the immune response for distinct transmission functions, in the presence of saturated CTL response. We compute the reproduction number of the model and state the stability of the disease-free equilibrium. We discuss the results of the model from an epidemiological point of view.
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页数：13
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共 34 条
  • [11] De Boer RJ, 2007, J VIROL, V81, P2838, DOI 10.1128/JVI.01914-06
  • [12] Solving a fractional order model of HIV infection of CD4+ T cells
    Gokdogan, Ahmet
    Yildirim, Ahmet
    Merdan, Mehmet
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) : 2132 - 2138
  • [13] Long-term HIV dynamics subject to continuous therapy and structured treatment interruptions
    Hadjiandreou, Marios M.
    Conejeros, Raul
    Wilson, D. Ian
    [J]. CHEMICAL ENGINEERING SCIENCE, 2009, 64 (07) : 1600 - 1617
  • [14] Global properties for virus dynamics model with Beddington-DeAngelis functional response
    Huang, Gang
    Ma, Wanbiao
    Takeuchi, Yasuhiro
    [J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (11) : 1690 - 1693
  • [15] The role of fractional calculus in modeling biological phenomena: A review
    Ionescu, C.
    Lopes, A.
    Copot, D.
    Machado, J. A. T.
    Bates, J. H. T.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 51 : 141 - 159
  • [16] A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems
    Jahanshahi, Salman
    Torres, Delfim F. M.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 174 (01) : 156 - 175
  • [17] A new numerical algorithm for fractional Fitzhugh-Nagumo equation arising in transmission of nerve impulses
    Kumar, Devendra
    Singh, Jagdev
    Baleanu, Dumitru
    [J]. NONLINEAR DYNAMICS, 2018, 91 (01) : 307 - 317
  • [18] Asymptotic properties of a HIV-1 infection model with time delay
    Li, Dan
    Ma, Wanbiao
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (01) : 683 - 691
  • [19] Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control
    Lizzy, R. Mabel
    Balachandran, Krishnan
    Trujillo, Juan J.
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 102 : 162 - 167
  • [20] On the numerical solution of the model for HIV infection of CD4+ T cells
    Merdan, Mehmet
    Gokdogan, Ahmet
    Yildirim, Ahmet
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (01) : 118 - 123
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