Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions

P Unni, P Seshaiyer - Computational and mathematical …, 2019 - Wiley Online Library
Over the last few decades, there have been significant developments in theoretical,
experimental, and clinical approaches to understand the dynamics of cancer cells and their …

Modeling tumor–immune dynamics

LG de Pillis, AE Radunskaya - … models of tumor-immune system dynamics, 2014 - Springer
Mathematical models of tumor–immune interactions provide an analytical framework in
which to address specific questions regarding tumor–immune dynamics and tumor treatment …

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 …

Qualitative behavior of systems of tumor–CD4+–cytokine interactions with treatments

L Anderson, S Jang, JL Yu - Mathematical Methods in the …, 2015 - Wiley Online Library
Immunotherapies are important methods for controlling and curing malignant tumors. Based
on recent observations that many tumors have been immuno‐selected to evade recognition …

Dynamics of tumor–CD4+–cytokine–host cells interactions with treatments

X Hu, SRJ Jang - Applied Mathematics and Computation, 2018 - Elsevier
Mathematical models of interactions between tumor cells, CD4+ T cells, cytokines, and host
cells are proposed to investigate the role of CD4+ on tumor regression. Our results suggest …

Mathematical modeling of tumor growth and treatment

H Enderling, M AJ Chaplain - Current pharmaceutical design, 2014 - ingentaconnect.com
Using mathematical models to simulate dynamic biological processes has a long history.
Over the past couple of decades or so, quantitative approaches have also made their way …

Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations

LG de Pillis, W Gu, AE Radunskaya - Journal of theoretical biology, 2006 - Elsevier
We develop and analyze a mathematical model, in the form of a system of ordinary
differential equations (ODEs), governing cancer growth on a cell population level with …

A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy

X Liu, Q Li, J Pan - Physica A: Statistical Mechanics and its Applications, 2018 - Elsevier
Modern medical studies show that chemotherapy can help most cancer patients, especially
for those diagnosed early, to stabilize their disease conditions from months to years, which …

Improving cancer treatments via dynamical biophysical models

M Kuznetsov, J Clairambault, V Volpert - Physics of life reviews, 2021 - Elsevier
Despite significant advances in oncological research, cancer nowadays remains one of the
main causes of mortality and morbidity worldwide. New treatment techniques, as a rule …

[PDF][PDF] Tumor dynamics modeling based on formal reaction kinetics

DA Drexler, T Ferenci, A Lovrics… - Acta Polytechnica …, 2019 - researchgate.net
Modeling the effect of therapeutic drugs on tumor dynamics is a fundamental step that leads
to the optimization of cancer therapy using mathematical tools. We discuss three tumor …