Related papers: A contact process with stronger mutations on trees
We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge $e^*$ is removed, one obtains two subtrees in which the contact process with infection rate smaller…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $\lambda>0$. With probability $p \in [0,1]$ an offspring is fertile…
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
We present a stochastic model for the size of a taxon in paleobiology, in which we allow for the evolution of new taxon members, and both individual and catastrophic extinction events. The model uses ideas from the theory of birth and death…
Oncolytic virotherapy, utilizing genetically modified viruses to combat cancer and trigger anti-cancer immune responses, has garnered significant attention in recent years. In our previous work arXiv:2305.12386, we developed a stochastic…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…
Movement behavior of biological entities plays a crucial role in their destiny through regulating their intraspecific and interspecific interactions as well as their interaction with surrounding environment. In spite of various models for…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
The shape of an epidemic wave in simple epidemic models applies to a homogeneous distribution of infected people in the population. In large inhomogeneous systems, at country-scale for instance, the wave shape is similar except for the…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a…