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We study a spatially inhomogeneous model of cancer growth based on Michaelis--Menten kinetics, subjected to additive Gaussian noise and multiplicative dichotomous noise. In presence of the latter, we can observe a transition between two…

Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…

There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant…

In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…

We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…

In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…

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…

We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a…

Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…

Mounting evidence underscores the prevalent hierarchical organization of cancer tissues. At the foundation of this hierarchy reside cancer stem cells, a subset of cells endowed with the pivotal role of engendering the entire cancer tissue…

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…

In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…

In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the…

We consider the impact of surface hydrodynamics on the interplay between curvature and composition in coarsening processes on model systems for biomembranes. This includes scaling laws and equilibrium configurations, which are investigated…

In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation…

One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical…

Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on…

In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…