Mathematical modeling as a tool for planning anticancer therapy

A Swierniak, M Kimmel, J Smieja - European journal of pharmacology, 2009 - Elsevier
We review a large volume of literature concerning mathematical models of cancer therapy,
oriented towards optimization of treatment protocols. The review, although partly …

A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences

A d'Onofrio - Physica D: Nonlinear Phenomena, 2005 - Elsevier
In this work we propose and investigate a family of models, which admits as particular cases
some well known mathematical models of tumor-immune system interaction, with the …

Antiangiogenic therapy in cancer treatment as an optimal control problem

U Ledzewicz, H Schättler - SIAM Journal on Control and Optimization, 2007 - SIAM
Antiangiogenic therapy is a novel treatment approach in cancer therapy that aims at
preventing a tumor from develo** its own blood supply system that it needs for growth. In …

On optimal delivery of combination therapy for tumors

A d'Onofrio, U Ledzewicz, H Maurer… - Mathematical …, 2009 - Elsevier
A mathematical model for the scheduling of angiogenic inhibitors in combination with a
chemotherapeutic agent is formulated. Conditions are given that allow tumor eradication …

Mathematical modeling of tumor-immune competitive system, considering the role of time delay

S Khajanchi, JJ Nieto - Applied mathematics and computation, 2019 - Elsevier
In this paper, we consider a three-dimensional nonlinear delay differential system (tumor
cells, cytotoxic-T lymphocytes, T-helper cells) with single interaction delay. We perform …

Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function

M Engelhart, D Lebiedz, S Sager - Mathematical biosciences, 2011 - Elsevier
In this article, four different mathematical models of chemotherapy from the literature are
investigated with respect to optimal control of drug treatment schedules. The various models …

[HTML][HTML] Cancer model and its possible control-a Z-type control approach

S Samanta, S Sarkar, K Kayal - MethodsX, 2024 - Elsevier
This paper investigates the dynamics of a three-dimensional nonlinear cancer model
involving interactions among cancer cells, normal cells, and immune cells. By performing a …

How tumor growth can be influenced by delayed interactions between cancer cells and the microenvironment?

D Ghosh, S Khajanchi, S Mangiarotti, F Denis… - BioSystems, 2017 - Elsevier
Although recent advances in oncology emphasized the role of microenvironment in tumor
growth, the role of delays for modeling tumor growth is still uncertain. In this paper, we …

[HTML][HTML] Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations

Y Deng, M Liu - Applied Mathematical Modelling, 2020 - Elsevier
In this article, an impulsive stochastic tumor-immune model with regime switching is
formulated and explored. Firstly, it is proven that the model has a unique global positive …

[HTML][HTML] Metamodeling tumor–immune system interaction, tumor evasion and immunotherapy

A d'Onofrio - Mathematical and Computer Modelling, 2008 - Elsevier
The tumor–immune system competitive interaction is very complex, being nonlinear and, to
some extent, evolutive. Furthermore, the tumor itself is not a single well defined disease, but …