Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 282–295 | Cite as

A model for interactions between immune cells and HIV considering drug treatments

  • Dayse H. Pastore
  • Roberto C. A. Thomé
  • Claudia M. Dias
  • Edilson F. Arruda
  • Hyun M. Yang


In this work, we analyze the capacity of the human body to combat HIV. The model here treated takes into consideration four types of defense of an organism infected by HIV: susceptible defense cells, the infected immune cells, killer T cells, and the HIV-specific killer T cells. This model, therefore, analyzes the interactions between the responses of killer T cells and HIV infections, evidencing how the immune system is attacked and how it defends. An optimal control problem is proposed to derive an optimal sequence of dosages in the standard drug treatment, in such a way as to minimize the side effects.


HIV Mathematical modelling Optimal control 

Mathematics Subject Classification

97M10 49J15 97M40 



This work was partially supported by the Carlos Chagas Filho Foundation for Research Support of the State of Rio de Janeiro, FAPERJ, under Grant no. E-26/202.789/2015, and by the Brazilian National Research Council-CNPq, under Grants 303543/2015-9.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Dayse H. Pastore
    • 1
  • Roberto C. A. Thomé
    • 1
  • Claudia M. Dias
    • 2
  • Edilson F. Arruda
    • 3
  • Hyun M. Yang
    • 4
  1. 1.Centro Federal de Educação Tecnológica Celso Suckow da FonsecaRio de JaneiroBrasil
  2. 2.Universidade Federal Rural do Rio de JaneiroNova IguaçuBrasil
  3. 3.Instituto Alberto Luiz Coimbra de Pós Graduação e Pesquisa de Engenharia, Programa de Engenharia de ProduçãoUniversidade Federal do Rio de JaneiroRio de JaneiroBrasil
  4. 4.Universidade Estadual de CampinasCampinasBrasil

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