A miscellany of new strategies, experimental techniques and theoretical approaches are
emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking …

This Timeline article charts progress in mathematical modelling of cancer over the past 50
years, highlighting the different theoretical approaches that have been used to dissect the …

Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

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 …

This is the first paper in a two-part series in which we develop, analyze, and simulate a
diffuse interface continuum model of multispecies tumor growth and tumor-induced …

In this paper the theory of mixtures is used to develop a two‐phase model of an avascular
tumour, which comprises a solid, cellular, phase and a liquid phase. Mass and momentum …

Mathematical modeling, analysis and simulation are set to play crucial roles in explaining
tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial …

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical
forces and other factors at different stages and in different environments is still largely …

This paper presents a critical review of selected topics related to the modelling of cancer
onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical …

We develop a thermodynamically consistent mixture model for avascular solid tumor growth
which takes into account the effects of cell-to-cell adhesion, and taxis inducing chemical and …