This review will outline a number of illustrative mathematical models describing the growth
of avascular tumors. The aim of the review is to provide a relatively comprehensive list of …

In the past 30 years we have witnessed an extraordinary progress on the research in the
molecular biology of cancer, but its medical treatment, widely based on empirically …

We develop a discrete model of malignant invasion using a thermodynamic argument. An
extension of the Potts model is used to simulate a population of malignant cells experiencing …

A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and
death is presented. The model qualitatively reproduces commonly observed morphologies …

Quantitative modelling is increasingly important in cancer research, hel** to integrate
myriad diverse experimental data into coherent pictures of the disease and able to …

The process by which one may take a discrete model of a biophysical process and construct
a continuous model based upon it is of mathematical interest as well as being of practical …

In this paper, we investigate stochastic bifurcation for a tumor–immune system in the
presence of a symmetric non-Gaussian Lévy noise. Stationary probability density functions …

Background Fractal geometry estimates have proven useful in studying the growth strategies
of fungi in response to different environments on soil or on agar substrates, but their use in …

Tumor growth has long been a target of investigation within the context of mathematical and
computer modeling. The objective of this study is to propose and analyze a two-dimensional …

Recently, we have proposed a nutrient-limited model for the avascular growth of tumors
including cell proliferation, motility, and death [SC Ferreira, Jr., ML Martins, and MJ Vilela …