Cancer immunotherapy, mathematical modeling and optimal control

F Castiglione, B Piccoli - Journal of theoretical Biology, 2007 - Elsevier
Clinical immunologists, among other problems, routinely face a question: what is the best
time and dose for a certain therapeutic agent to be administered to the patient in order to …

Optimal response to chemotherapy for a mathematical model of tumor–immune dynamics

U Ledzewicz, M Naghnaeian, H Schättler - Journal of mathematical …, 2012 - Springer
An optimal control problem for cancer chemotherapy is considered that includes
immunological activity. In the objective a weighted average of several quantities that …

Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls

LG de Pillis, W Gu, KR Fister, TA Head, K Maples… - Mathematical …, 2007 - Elsevier
We investigate a mathematical model of tumor–immune interactions with chemotherapy, and
strategies for optimally administering treatment. In this paper we analyze the dynamics of …

Immunotherapy: an optimal control theory approach

KR Fister, JH Donnelly - Mathematical Biosciences & Engineering, 2005 - aimsciences.org
We investigate mathematical models for the dynamics between tumor cells, immune-effector
cells, and cytokine interleukin-2 (IL-2). To better determine under what circumstances the …

On the global dynamics of a model for tumor immunotherapy

DE Kirschner, A Tsygvintsev - Mathematical Biosciences & …, 2009 - aimsciences.org
Understanding the dynamics of human hosts and tumors is of critical importance. A
mathematical model was developed that explored the immune response to tumors that was …

Determination of the optimal therapeutic protocols in cancer immunotherapy

A Cappuccio, F Castiglione, B Piccoli - Mathematical biosciences, 2007 - Elsevier
Cancer immunotherapy aims at eliciting an immune system response against the tumor.
However, it is often characterized by toxic side-effects. Limiting the tumor growth and …

Optimal control of drug therapy in cancer treatment

M Itik, MU Salamci, SP Banks - Nonlinear Analysis: Theory, Methods & …, 2009 - Elsevier
We present an optimal control strategy for nonlinear systems with application to the drug
therapy of cancer. The tumour growth model is represented by a system of equations from …

[PDF][PDF] Optimal control applied to immunotherapy

TN Burden, J Ernstberger, KR Fister - Discrete and Continuous …, 2004 - researchgate.net
We investigate a mathematical model for the dynamics between tumor cells, immune-
effector cells, and the cytokine interleukin-2 (IL-2). In order to better determine under what …

Optimal control of mixed immunotherapy and chemotherapy of tumors

LG de Pillis, KR Fister, W Gu, T Head… - Journal of Biological …, 2008 - World Scientific
We investigate a mathematical population model of tumor-immune interactions. The
populations involved are tumor cells, specific and non-specific immune cells, and …

Optimal control for mathematical models of cancer therapies

H Schättler, U Ledzewicz - An application of geometric methods, 2015 - Springer
Cancer is a highly complex disease with a myriad of different manifestations. The reasons
for this simply lie not only in the many types of different cells that exist in our bodies, but also …