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
  • [1] Solutions of Bagley-Torvik and Painlev, equations of fractional order using iterative reproducing kernel algorithm with error estimates
    Abu Arqub, Omar
    Maayah, Banan
    [J]. NEURAL COMPUTING & APPLICATIONS, 2018, 29 (05) : 1465 - 1479
  • [2] Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations
    Abu Arqub, Omar
    El-Ajou, Ahmad
    Momani, Shaher
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 385 - 399
  • [3] Ammi M.R.S., 2017, ADV DIFFER EQU, V2017, P1
  • [4] [Anonymous], 2017, PROGR FRACT DIFFER A
  • [5] Dynamics of cytotoxic T-lymphocytes and helper cells in human immunodeficiency virus infection with Hill-type infection rate and sigmoidal CTL expansion
    Bairagi, Nandadulal
    Adak, Debadatta
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 103 : 52 - 67
  • [6] Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection
    Burg, David
    Rong, Libin
    Neumann, Avidan U.
    Dahari, Harel
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 2009, 259 (04) : 751 - 759
  • [7] Non-integer order analysis of the impact of diabetes and resistant strains in a model for TB infection
    Carvalho, Ana R. M.
    Pinto, Carla M. A.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 61 : 104 - 126
  • [8] HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load
    Carvalho, Ana R. M.
    Pinto, Carla M. A.
    Baleanu, Dumitru
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [9] Within-host and synaptic transmissions: contributions to the spread of HIV infection
    Carvalho, Ana R. M.
    Pinto, Carla M. A.
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (04) : 1231 - 1264
  • [10] Reducing bias in fractional order impedance estimation for lung function evaluation
    Copot, Dana
    De Keyser, Robin
    Derom, Eric
    Ortigueira, Manuel
    Ionescu, Clara M.
    [J]. BIOMEDICAL SIGNAL PROCESSING AND CONTROL, 2018, 39 : 74 - 80
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