Related papers: Dynamics and bifurcations in a simple quasispecies…

Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…

We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…

We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…

Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…

Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…

Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…

Tumor development is an evolutionary process in which a heterogeneous population of cells with differential growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to…

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…

Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the…

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…

Cancer has been characterized as a constellation of hundreds of diseases differing in underlying mutations and depending on cellular environments. Carcinogenesis as a stochastic physical process has been studied for over sixty years, but…

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…

Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…

Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as…

We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly,we develop it taking into account periodical immunotheraphy treatment with cytokines…

In this work, we develop a kinetic model of tumour growth taking into account the effects of clinical uncertainties characterising the tumours' progression. The action of therapeutic protocols trying to steer the tumours' volume towards a…

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…