Related papers: Large Deviations of Cancer Recurrence Timing
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated…
For the M/M/1+M model at the law-of-large-numbers scale, the long run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbr\"uck model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for…
Adaptive therapy is a promising paradigm for treating cancers, that exploits competitive interactions between drug-sensitive and drug-resistant cells, thereby avoiding or delaying treatment failure due to evolution of drug resistance within…
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
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…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
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…
This paper focuses on the analytic modelling of responses of cells in the body to ionizing radiation. The related mechanisms are consecutively taken into account and discussed. A model of the dose- and time-dependent adaptive response is…
Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population…
The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta…
The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…
Individual cells exhibit specific proliferative responses to changes in microenvironmental conditions. Whether such potential is constrained by the cell density throughout the growth process is however unclear. Here, we identify a…
Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The…
Populations can evolve in order to adapt to external changes. The capacity to evolve and adapt makes successful treatment of infectious diseases and cancer difficult. Indeed, therapy resistance has quickly become a key challenge for global…
This paper considers the Cram\'er-Lundberg model, with the additional feature that the number of clients can fluctuate over time. Clients arrive according to a Poisson process, where the times they spend in the system form a sequence of…