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The adaptive immune system relies on the diversity of receptors expressed on the surface of B and T-cells to protect the organism from a vast amount of pathogenic threats. The proliferation and degradation dynamics of different cell types…

Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…

We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a now classic approach, the first stage of the invasion is…

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…

Understanding the role of microenvironment in cancer growth and metastasis is a key issue for cancer research. Here, we study the effect of osmotic pressure on the functional properties of primary and metastatic melanoma cell lines. In…

Controlling growth via cell division is crucial in the development of higher organisms, and yet the mechanisms through which this is achieved, e.g., in epithelial tissue, is not yet fully understood. We show that by coupling the cell cycle…

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…

Control of cell proliferation is a fundamental aspect of tissue physiology central to morphogenesis, wound healing and cancer. Although many of the molecular genetic factors are now known, the system level regulation of growth is still…

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…

Any process in which competing solutions replicate with errors and numbers of their copies depend on their respective fitnesses is the evolutionary optimization process. As during carcinogenesis mutated genomes replicate according to their…

The site frequency spectrum (SFS) is a popular summary statistic of genomic data. While the SFS of a constant-sized population undergoing neutral mutations has been extensively studied in population genetics, the rapidly growing amount of…

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…

Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…

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 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…

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight…

Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in…

Cancers are caused by the accumulation of genetic alterations. Since this accumulation takes time, the incidence of most cancers is thought to increase exponentially with age. However, careful measurements of the age-specific incidence…

Tumours are made up of a mixed population of different types of cells that include normal struc- tures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local…