An Optimal Control Approach to HIV Immunology

Author(s):Edilson F. Arruda, Claudia M. Dias, Camila V. de Magalhães, Dayse H. Pastore, Roberto C. A. Thomé, Hyun Mo Yang

This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient’s medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin’s Maximum Principle.


Journal: Applied Mathematics
DOI: 10.4236/am.2015.66102

Paper Id: 57139 (metadata)

See also: Comments to Paper

About scirp

(SCIRP: is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in AM and tagged , , , . Bookmark the permalink.

Comments are closed.