Analysis and control of an age-structured HIV-1 epidemic model with different transmission mechanisms

Wang, Xiaoyan; Yang, Junyuan; Xu, Fei

doi:10.1186/s13662-017-1455-0

Cited by 1 publication

(1 citation statement)

References 33 publications

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“…Within a certain period of treatment, we expect to achieve the concentration of uninfected CD4+T cells and CTLs as large as possible and the drug side effect as small as possible by controlling the efficiency of RTIs and PIs. Recently, previous researches 20,21 show that PIs can effectively block cell‐to‐cell transmission of HIV, whereas RTIs are less effective inhibitors for cell‐to‐cell transmission compared with cell‐free infection. Based on system () and previous literature, 20,21 we propose the following model:

({, \begin{array}{l} \frac{dT}{dt} = s - μ_{T} T ((), t) - ([], 1 - u_{1} ((), t - ε_{1})) k_{1} T ((), t) V ((), t) - ([], 1 - κ u_{2} ((), t - ε_{3})) k_{2} T ((), t) T^{*} ((), t), \\ \frac{{italicdT}^{*}}{dt} = ([], 1 - u_{1} ((), t - ε_{1})) k_{1} T ((), t - τ) V ((), t - τ) e^{- italicδτ} - μ_{T^{*}} T^{*} ((), t) - k_{3} C ((), t) T^{*} ((), t) \\ \begin{matrix} center \end{matrix} + ([], 1 - κ u_{2} ((), t - ε_{3})) k_{2} T ((), t - τ) T^{*} ((), t - τ) e^{- italicδτ}, \\ \frac{dV}{dt} = ([], 1 - u_{2} ((), t - ε_{2})) N μ_{T^{*}} T^{*} ((), t) - μ_{v} V ((), t), \\ \frac{dC}{dt} = italicaT ((), t) T^{*} ((), t) C ((), t) - μ_{c} C ((), t), \end{array})

where ...…”

Section: Optimal Controlmentioning

confidence: 99%

Analysis and control of a delayed HIV infection model with cell‐to‐cell transmission and cytotoxic T lymphocyte immune response

Liu

Lin

2021

Math Methods in App Sciences

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Recent researches show that virus‐to‐cell infection and cell‐to‐cell transmission are two HIV infection modes. In this paper, we propose a delayed HIV infection model including both virus‐to‐cell infection and cell‐to‐cell transmission and cytotoxic T lymphocyte immune response. The time delay describes the phenomenon between viral entry and viral production. We show the nonnegativity and boundedness of solution, obtain the steady states, and prove local asymptotic stability of the steady states. Then the optimal control problem with antiretroviral therapy and pharmacological delay is posed. We establish and analyze two types of objective functions: one is linear control and the other is quadratic control. Numerical simulations have been performed to verify the stability of steady states and show the optimal control strategies and the effects of control on cells concentration by Matlab and Lingo.

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