Resumo

TORO-ZAPATA, Hernán Darío  e  TRUJILLO-SALAZAR, Carlos Andrés. HIV optimal control model with infection rate depending on the virus density. Rev. Mat [online]. 2018, vol.25, n.2, pp.261-292. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v25i2.33625.

[17]

We propose a model on ordinary differential equations to describe the dynamics of HIV infection in a population of CD4 T cells susceptible to infection and considering a nonlinear infection rate depending on viral density. The stability of the model is analyzed based on the basic reproduction number, which allows us to determine stability results and a control threshold by reducing the rate of maximum infection. An optimal control problem is then formulated to establish optimal treatment functions by reverse transcriptase inhibitors and protease inhibitors that minimize viral load and direct and/or indirect costs of treatment administration. We study the cases in which the effectiveness of the treatment is null and full, and for the case of imperfect effectiveness of the treatment, we refer to the MaximumPrincipleofPontryagin. Numerical simulations of the model without treatment and of the different scenarios with treatment are presented.

Palavras-chave : dynamic system; stability; optimal control; Pontryagin maximum principle; HIV; antirretroviral therapy.

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