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 …
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 …
some well known mathematical models of tumor-immune system interaction, with the …
Antiangiogenic therapy in cancer treatment as an optimal control problem
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 …
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 mathematical model for the scheduling of angiogenic inhibitors in combination with a
chemotherapeutic agent is formulated. Conditions are given that allow tumor eradication …
chemotherapeutic agent is formulated. Conditions are given that allow tumor eradication …
Mathematical modeling of tumor-immune competitive system, considering the role of time delay
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 …
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
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 …
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
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 …
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?
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 …
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 …
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 …
some extent, evolutive. Furthermore, the tumor itself is not a single well defined disease, but …