Related papers: A host-parasite model for a two-type cell populati…
How is the progression of a virus influenced by properties intrinsic to individual cells? We address this question by studying the susceptibility of cells infected with two strains of the human respiratory syncytial virus (RSV-A and RSV-B)…
We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterisation of symbiotic relations of coexisting species through their mutual influence on their respective…
We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the microbial hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a contact-mediated…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
Eigen's quasi-species model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature…
This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
We propose a type-dependent branching model with mutation and competition for modeling phylogenies of a virus population. The competition kernel depends for any two virus particles on the particles' types, the total mass of the population…
To examine the co-evolution of quantitative traits in hosts and parasites, we present and study a co-evolutionary model of a social parasite-host system that incorporates (1) ecological dynamics that feed back into their co-evolutionary…
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…
Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space…
Vector-borne diseases often infect multiple host species, increasing the likelihood of disease persistence due to the presence of multiple reservoirs. Vector biting patterns and feeding preferences can shift in response to selective…
Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…
The emergence or adaptation of pathogens may lead to epidemics, highlighting the need for a thorough understanding of pathogen evolution. The tradeoff hypothesis suggests that virulence evolves to reach an optimal transmission intensity…
In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…