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Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…
We investigate noise-induced pattern formation in a model of cancer growth based on Michaelis-Menten kinetics, subject to additive and multiplicative noises. We analyse stability properties of the system and discuss the role of diffusion…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
Tumor recurrence, driven by the evolution of drug resistance is a major barrier to therapeutic success in cancer. Resistance is often caused by genetic alterations such as point mutation, which refers to the modification of a single genomic…
A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…
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…
Research into somatic mutations in cancer cell DNA and their role in tumour growth and progression between successive stages is crucial for improving our understanding of cancer evolution. Mathematical and computer modelling can provide…
Cancer results from a sequence of genetic and epigenetic changes which lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells, and thus, to a selective advantage of pre-cancerous cells. The…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…
The dynamics of tumour evolution are not well understood. In this paper we provide a statistical framework for evaluating the molecular variation observed in different parts of a colorectal tumour. A multi-sample version of the Ewens…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…
Two models of circulating tumor cell (CTC) dynamics have been proposed to explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the primary tumor and accelerate growth: Primary Seeding, where cells from a primary tumor…
Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1…
We report on a simple model of spatial extend anti-tumor system with a fluctuation in growth rate, which can undergo a nonequilibrium phase transition. Three states as excited, sub-excited and non-excited states of a tumor are defined to…
We study large deviation events in the timing of disease recurrence. In particular, we are interested in modeling cancer treatment failure due to mutation-induced drug resistance. We first present a two-type branching process model of this…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…