Towards a unified approach in the modeling of fibrosis: A review with research perspectives

MB Amar, C Bianca - Physics of life reviews, 2016 - Elsevier
Pathological fibrosis is the result of a failure in the wound healing process. The
comprehension and the related modeling of the different mechanisms that trigger fibrosis are …

A quantitative cellular automaton model of in vitro multicellular spheroid tumour growth

MJ Piotrowska, SD Angus - Journal of theoretical biology, 2009 - Elsevier
We report numerical results from a 2D cellular automaton (CA) model describing the
dynamics of the in vitro cultivated multicellular spheroid obtained from EMT6/Ro (mammary …

Analysis of the Hopf bifurcation for the family of angiogenesis models

MJ Piotrowska, U Foryś - Journal of Mathematical Analysis and …, 2011 - Elsevier
In this paper we study a family of models with delays describing the process of
angiogenesis, that is a physiological process involving the growth of new blood vessels from …

Mathematical modelling of immune reaction against gliomas: Sensitivity analysis and influence of delays

MJ Piotrowska, M Bodnar, J Poleszczuk… - Nonlinear Analysis: Real …, 2013 - Elsevier
In the paper we considered a model of immune reaction against malignant glioma. The
model proposed by Kronik et al.(Cancer Immunol. Immunother., 2008) describes simplified …

The time delays' effects on the qualitative behavior of an economic growth model

C Bianca, M Ferrara, L Guerrini - Abstract and applied analysis, 2013 - Wiley Online Library
A further generalization of an economic growth model is the main topic of this paper. The
paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when …

Analysis of a solid avascular tumor growth model with time delays in proliferation process

S Xu, M Bai, X Zhao - Journal of Mathematical Analysis and Applications, 2012 - Elsevier
In this paper we study a free boundary problem modeling solid avascular tumor growth. The
model is based on the reaction–diffusion dynamics and mass conservation law. The model …

Analysis of a free boundary problem for tumor growth with angiogenesis and time delays in proliferation

S Xu - Nonlinear Analysis: Real World Applications, 2020 - Elsevier
In this paper we consider a free boundary problem for tumor growth with angiogenesis and
time delays in the process of proliferation. The model is established by using reaction …

Analysis of a free boundary problem for vascularized tumor growth with a necrotic core and time delays

S Xu, Z Xuan - Nonlinear Analysis: Real World Applications, 2023 - Elsevier
In this paper a free boundary problem for vascularized tumor growth with a necrotic core and
time delays is studied. In the problem, there are two free boundaries, one is the outer …

[HTML][HTML] Analysis of tumor-immune dynamics in a delayed dendritic cell therapy model

LR Dickman, Y Kuang - Chaos: An Interdisciplinary Journal of …, 2020 - pubs.aip.org
We formulate a tumor-immune interaction model with a constant delay to capture the
behavior following application of a dendritic cell therapy. The model is validated using …

Hopf bifurcation of a free boundary problem modeling tumor growth with angiogenesis and two time delays

H Zhou, Z Wang, D Yuan, H Song - Chaos, Solitons & Fractals, 2021 - Elsevier
This paper concerns a free boundary problem modeling tumor growth with angiogenesis
and two time delays. The two delays represent the time taken for cells to undergo mitosis …