Related papers: A stochastic model for virus growth in a cell popu…
We propose an epidemic model for the spread of vector-borne diseases. The model, which is built extending the classical susceptible-infected-susceptible model, accounts for two populations -- humans and vectors -- and for cross-contagion…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
We introduce an Ising approach to study the spread of malware. The Ising spins up and down are used to represent two states--online and offline--of the nodes in the network. Malware is allowed to propagate amongst online nodes and the rate…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
One of the most promising strategies to treat cancer is attacking it with viruses. Virus can kill tumor cells specifically or act as carriers that deliver normal genes into cancer cells. A model for virus therapy of cancer is investigated…
Cells achieve size homeostasis by regulating their division timing based on their size, added size, and cell cycle time. Previous research under steady-state conditions demonstrated the robustness of these mechanisms. However, their dynamic…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We propose a Markov model for the spread of Hepatitis C virus (HCV) among drug users who use injections. We then proceed to an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a non…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are…
We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…
We employ the framework of multitype Galton-Watson processes to model a population of dividing cells. The cellular type is represented by its biological age, defined as the count of harmful proteins hosted by the cell. The stochastic…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
Recent work on information survival in sensor and human P2P networks, try to study the datum preservation or the virus spreading in a network under the dynamical system approach. Some interesting solutions propose to use non-linear…
Inspired by DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts. The parasite is capable to persist in its host till the host dies, and to reinfect other hosts. To maintain…
We present a novel model that describes the within-host evolutionary dynamics of parasites undergoing antigenic variation. The approach uses a multi-type branching process with two types of entities defined according to their relationship…
We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of…