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Although optimal control theory has been used for the theoretical study of anti-cancerous drugs scheduling optimization, with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously…

Tissues and Organs · Quantitative Biology 2013-06-21 Sebastien Benzekry , Philip Hahnfeldt

We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the…

Analysis of PDEs · Mathematics 2019-02-06 Anderson L. A. de Araujo , Artur C. Fassoni , Luís F. Salvino

We mathematically justify metronomic chemotherapy as the best strategy to apply most cytotoxic drugs in oncology for both curative and palliative approaches, assuming the classical pharmacokinetic model together with the Emax…

Optimization and Control · Mathematics 2021-10-15 Luis A. Fernández , Cecilia Pola , Judith Sáinz-Pardo

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

Analysis of PDEs · Mathematics 2015-03-31 Donatella Donatelli , Konstantina Trivisa

Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…

Quantitative Methods · Quantitative Biology 2024-07-09 Carlos M. Nieto , Oscar M. Pimentel , Fabio D. Lora-Clavijo

The combination of cytotoxic therapies and anti-angiogenic agents is emerging as a most promising strategy in the treatment of malignant tumors. However, the timing and sequencing of these treatments seem to play essential roles in…

Tissues and Organs · Quantitative Biology 2011-06-13 M. Kohandel , C. A. Haselwandter , M. Kardar , S. Sengupta , S. Sivaloganathan

Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}.…

Condensed Matter · Physics 2009-11-07 S. C. Ferreira , M. L. Martins , M. J. Vilela

We continue our study of a model for cancer treatment, constructed in Dutta et. al., 2025, by adding Virotherapy to the Chemotherapy and Immunotherapy studied there. It is a dynamical system model for the spread of cancer in healthy tissue.…

Other Quantitative Biology · Quantitative Biology 2026-03-02 Tarini Kumar Dutta , Silmera A Sangma , Janice Moore , Meir Shillor

We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a…

Analysis of PDEs · Mathematics 2020-10-22 Tania Biswas , Elisabetta Rocca

We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…

Optimization and Control · Mathematics 2016-08-02 Harald Garcke , Kei-Fong Lam , Elisabetta Rocca

Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…

Tissues and Organs · Quantitative Biology 2026-05-19 Yuhong Zhang , Chenghang Li , Boya Wang , Jinzhi Lei

Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully…

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor…

Cell Behavior · Quantitative Biology 2013-05-17 Kathleen P. Wilkie , Philip Hahnfeldt

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…

Optimization and Control · Mathematics 2025-03-13 Bouhamidi Abderrahman , El Harraki Imad , Melouani Yassine

We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…

Numerical Analysis · Mathematics 2016-02-23 Konstantina Trivisa , Franziska Weber

Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…

Tissues and Organs · Quantitative Biology 2007-05-23 Benjamin Ribba , Thierry Colin , Santiago Schnell

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 additional assumption that the influx of immune system cells may…

Tissues and Organs · Quantitative Biology 2015-06-17 Alberto d'Onofrio

We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the…

This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population…

Optimization and Control · Mathematics 2018-12-26 Tuğba Akman Yıldız , Sadia Arshad , Dumitru Baleanu