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 …

A system of nonlinear partial differential equations is proposed as a model for the growth of
an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living …

We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl.
Med. Biol., 14, 39–69) by incorporating two necrotic depletion mechanisms, which results in …

Cancerous tumours have the ability to recruit new blood vessels through a process called
angiogenesis. By stimulating vascular growth, tumours get connected to the circulatory …

In this paper, we develop a simple mathematical model of the vascularization and
subsequent growth of a solid spherical tumour. The key elements that are encapsulated in …

There is a very strong link between the vascularization of a tumour and the spread of the
disease, both locally and to distant sites (Gimbrone et al., 1974, J. Natl. Cancer Inst. 52, 413 …

In this paper we present a new model framework for studying vascular tumour growth, in
which the blood vessel density is explicitly considered. Our continuum model comprises …

Cancer is a collection of diseases with the common feature of uncontrolled cellular growth.
Most tissues in the body can give rise to cancer, some even yield several types, and each …

Understanding tumor induced angiogenesis is a challenging problem with important
consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest …

During the past several years mathematical models have been applied to various aspects of
cancer dynamics, in particular avascular and vascular tumour growth, invasion …