A model for interactions between immune cells and HIV considering drug treatments
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A model for interactions between immune cells and HIV considering drug treatments Dayse H. Pastore1 · Roberto C. A. Thomé1 · Claudia M. Dias2 · Edilson F. Arruda3 · Hyun M. Yang4
Received: 28 March 2017 / Revised: 4 October 2017 / Accepted: 19 October 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract 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 HIVspecific 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. Keywords HIV · Mathematical modelling · Optimal control
Communicated by Jose Roberto Castilho Piqueira, Elbert E N Macau, Luiz de Siqueira Martins Filho.
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Edilson F. Arruda [email protected] Dayse H. Pastore [email protected] Roberto C. A. Thomé [email protected] Claudia M. Dias [email protected] Hyun M. Yang [email protected]
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Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Maracanã, 229, Rio de Janeiro, RJ 20271-110, Brasil
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Universidade Federal Rural do Rio de Janeiro, Av. Governador Roberto Silveira, s/n, Nova Iguaçu, RJ 26020-740, Brasil
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Instituto Alberto Luiz Coimbra de Pós Graduação e Pesquisa de Engenharia, Programa de Engenharia de Produção, Universidade Federal do Rio de Janeiro, Caixa Postal 68507, Rio de Janeiro, RJ 21941-972, Brasil
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Universidade Estadual de Campinas, Caixa Postal 6065, Campinas, SP, Brasil
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D. H. Pastore et al.
Mathematics Subject Classification 97M10 · 49J15 · 97M40
1 Introduction Mathematical models are essential tools in decision-making problems that arise in a wide range of areas. In particular, they provide the means for understanding population dynamics (e.g., Levin et al. 1997), which can be used as an abstraction to model epidemiological problems. According to Heesterbeek et al. (2015) “many factors, including increasing antimicrobial resistance, human connectivity, population growth, urbanization, environmental and land use change, as well as changing human behavior, present global challenges for prevention and control. Faced with this complexity, mathematical models offer valuable tools for understanding epidemiological patterns and for developing and evaluating evidence for decision-making in global health”. More specifically, Heesterbeek et al. (2015) provide an overview of the role of mathematical modeling in our understanding of the HIV epidemic, and in the decision-making process that followed. Such a role is also discussed in the excellent work of Perelson and Ribeiro (2013), which discusses the importance of modeling to uncover important characteristics
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