Immune Therapeutic Strategies Using Optimal Controls with $L^1$ and $L^2$ Type Objectives
Abstract
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an type objective functional as well as an type objective. For the former, the presence of singular control will be addressed. For each case, numerical simulations using a nonlinear programming optimization solver to acquire different drug treatment strategies are presented and discussed. The results provide insight for possible treatment strategies and the methods could be a relevant tool for future practice to assist in better prediction of clinical outcomes and subsequently better treatment for patients.
Keywords
Cite
@article{arxiv.1610.06655,
title = {Immune Therapeutic Strategies Using Optimal Controls with $L^1$ and $L^2$ Type Objectives},
author = {Ouassim Bara and Seddik Djouadi and Judy Day and Suzanne Lenhart},
journal= {arXiv preprint arXiv:1610.06655},
year = {2017}
}