Related papers: Computational tools for assessing gene therapy und…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
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…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support…
For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the…
Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are…
Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
Many areas of agriculture rely on honey bees to provide pollination services and any decline in honey bee numbers can impact on global food security. In order to understand the dynamics of honey bee colonies we present a discrete time…
Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan.…
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…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
Mutation is one of the most important stages of the genetic algorithm because of its impact on the exploration of global optima, and to overcome premature convergence. There are many types of mutation, and the problem lies in selection of…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We present a three-stage probabilistic model for the progression of Chronic Myeloid Leukemia (CML), as manifested by the leukemic stem cells, progenitor cells and mature leukemic cells. This progression is captured through the process of…
Despite initial success, cancer therapies often fail due to the emergence of drug-resistant cells. In this study, we use a mathematical model to investigate how cancer evolves over time, specifically focusing on the state of the tumor when…
This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…
We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the…
Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been…