Optimal control of tumour-immune model with time-delay and immuno-chemotherapy

F.A. Rihan, S. Lakshmanan and H. Maurer

Applied Mathematics and Computation, 2019, vol. 353, issue C, 147-165

Abstract: Herein, we study an optimal control problem of delay differential model to describe the dynamics of tumour-immune interactions in presence of immuno-chemotherapy. The model includes constant delays in the mitotic phase to justify the time required to stimulate the effector cells and for the effector cells to develop a suitable response to the tumour cells. By applying optimal control theory, we seek to minimize the cost associated with the immuno-chemotherapy and to reduce load of of tumour cells. Non-Negativity of the solutions of the model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are also discussed. We numerically approximate the solution of the optimal control problem by solving the state system forward and adjoint system backward in time. The numerical simulations show that the combination of immuno-chemotherapy protocol reduces the tumour load in few months of therapy.

Keywords: DDEs; Hamiltonian; Immuno-chemotherapy; Optimal control; Time-delay; Tumour cells; Stability (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319301006
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:353:y:2019:i:c:p:147-165

DOI: 10.1016/j.amc.2019.02.002

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().