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Nonlinear effects in the dynamics of HIV-1 infection predicted by mathematical model with multiple delays

  • * Corresponding author: Nikolay Pertsev

    * Corresponding author: Nikolay Pertsev 

The first and the last authors are supported by Russian Science Foundation grant 18-11-00171

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  • We formulate a novel mathematical model to describe the development of acute HIV-1 infection and the antiviral immune response. The model is formulated using a system of delay differential- and integral equations. The model is applied to study the possibility of eradication of HIV infection during the primary acute phase of the disease. To this end a combination of analytical examination and computational treatment is used. The model belongs to the Wazewski differential equation systems with delay. The conditions of asymptotic stability of a trivial steady state solution are expressed in terms of the algebraic Sevastyanov–Kotelyanskii criterion. The results of the computational experiments with the model calibrated according to the available estimates of parameters suggest that a complete elimination of HIV-1 infection after acute phase of infection is feasible.

    Mathematics Subject Classification: Primary: 97M60, 34K60; Secondary: 37N25, 92C99.

    Citation:

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  • Figure 1.  Schematic representation of the model of acute HIV-1 infection

    Figure 2.  Computational Experiment 1. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 0.9224 $, $ V^0 = 10^4 $

    Figure 3.  Computational Experiment 2. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 0.9073 $, $ V^0 = 10^4 $

    Figure 4.  Computational Experiment 3. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 2.2875 $. (a) $ V^0 = 10^4 $, (b) $ V^0 = 10^6 $

    Figure 5.  Computational Experiment 4. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 2.2875 $. (a) $ V^0 = 10^4 $, (b) $ V^0 = 10^6 $

    Figure 6.  Computational Experiment 5. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 13.2135 $. (a) $ V^0 = 10^2 $, (b) $ V^0 = 10^6 $

    Figure 7.  Computational Experiment 6. Dynamics of $ y_1(t) $, $ y_2(t) $, $ y_3(t) $ for $ R_0 = 3.3789 $. (a) $ V^0 = 10^4 $, (b) $ V^0 = 10^6 $

    Table 1.  Time post infection needed for a complete elimination of HIV-1 infection

    $ V_0 $ Computational experiment number, the value $ \tau_0 $ (day)
    1 2 3 4 5 6
    $ 10 $ 1 1 $ - $ $ - $ $ - $ 46
    $ 10^2 $ 51 46 $ - $ 51 $ - $ 44
    $ 10^4 $ 60 115 $ - $ 37 $ - $ 42
    $ 10^6 $ 67 132 76 78 102 53
    $ 10^7 $ 72 140 96 94 $ - $ 57
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