Immune therapeutic strategies using optimal controls with L^sup 1^ and L^sup 2^ type objectives

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 contro...

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Bibliographic Details
Published in:Mathematical biosciences 2017-08, Vol.290, p.9
Main Authors: Bara, O, Djouadi, SM, Day, JD, Lenhart, S
Format: Article
Language:English
Subjects:
Computer simulation
Immune response
Immune system
Inflammation
Inflammatory response
Mathematical models
Maximum principle
Medical treatment
Nonlinear programming
Optimal control
Optimization
Simulation
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Summary: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 L1 type objective functional as well as an L2 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.
ISSN:0025-5564
1879-3134