Related papers: Survival Probabilities at Spherical Frontiers
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…
We study the evolution of gene frequencies in a population living in $\mathbb{R}^d$, modelled by the spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge and Veber, 2010 and Etheridge, Veber and Yu, 2014). We…
The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…
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 study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a…
The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
This paper deals with a simplified SIS model, which describes the transmission of the disease in time-periodic heterogeneous environment. To understand the impact of spatial heterogeneity of environment and small advection on the…
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the…
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial…
We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm…
Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…
Phenotypic plasticity and its evolution may help evolutionary rescue in a novel and stressful environment, especially if environmental novelty reveals cryptic genetic variation that enables the evolution of increased plasticity. However,…