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We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…
The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps…
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We use a statistical physics model to study the evolution of a population of malignant…
Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were…
The emergence of acquired drug resistance in cancer represents a major barrier to treatment success. While research has traditionally focused on genetic sources of resistance, recent findings suggest that cancer cells can acquire transient…
Predicting cancer-associated clinical events is challenging in oncology. In Multiple Myeloma (MM), a cancer of plasma cells, disease progression is determined by changes in biomarkers, such as serum concentration of the paraprotein secreted…
Chronic diseases and cancer account for over 75 percent of healthcare costs in the US. Increased prevention services and improved primary care are thought to decrease costs. Current models for detecting changes in the health of populations…
It is increasingly common clinically for cancer specimens to be examined using techniques that identify somatic mutations. In principle these mutational profiles can be used to diagnose the tissue of origin, a critical task for the 3-5% of…
Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been proposed as models of the genealogy of $n$ sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's…
Recently, there has been a resurgence of interest in rigorous algorithms for the inference of cancer progression from genomic data. The motivations are manifold: (i) growing NGS and single cell data from cancer patients, (ii) need for novel…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell…
An endogenous molecular-cellular network for both normal and abnormal functions is assumed to exist. This endogenous network forms a nonlinear stochastic dynamical system, with many stable attractors in its functional landscape. Normal or…
The variation in DNA copy number carries information on the modalities of genome evolution and misregulation of DNA replication in cancer cells; its study can be helpful to localize tumor suppressor genes, distinguish different populations…
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…
Tumor cell populations can be thought of as being composed of homogeneous cell subpopulations, with each subpopulation being characterized by overlapping sets of single nucleotide variants (SNVs). Such subpopulations are known as subclones…
Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that…