Related papers: Cell contamination and branching process in random…
We present a model for host-parasite dynamics which incorporates both vertical and horizontal transmission as well as spatial structure. Our model consists of stacked contact processes (CP), where the dynamics of the host is a simple CP on…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
We study a stochastic epidemic model with multiple patches (locations), where individuals in each patch are categorized into three compartments, Susceptible, Infected and Recovered/Removed, and may migrate from one patch to another in any…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
Agent-based models of disease transmission involve stochastic rules that specify how a number of individuals would infect one another, recover or be removed from the population. Common yet stringent assumptions stipulate interchangeability…
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…
Certain defense mechanisms of phages against the immune system of their bacterial host rely on cooperation of phages. Motivated by this example we analyse invasion probabilities of cooperative parasites in host populations that are…
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…
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…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
Multipartite viruses replicate through a puzzling evolutionary strategy. Their genome is segmented into two or more parts, and encapsidated in separate particles that appear to propagate independently. Completing the replication cycle,…
There is a rich history of models for the interaction of a biological contagion like influenza with the spread of related information such as an influenza vaccination campaign. Recent work on the spread of interacting contagions on networks…
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the…
We consider a class of Crump-Mode-Jagers processes with interaction, constructed by removing a newly born offspring with a probability that depends on the age structure of the population at its birth time. We prove a law of large numbers…
We present a two-species population model in a well-mixed environment where the dynamics involves, in addition to birth and death, changes due to environmental factors and inter-species interactions. The novel dynamical components are…
Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur,…
Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions…
We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here orthogonal branching occurring always in the same direction.…
The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as…