Related papers: Population models with singular equilibrium
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin)…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…
Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies)…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the…
We study a slow-fast parasite--host model featuring a singularity at the extinction state. Using techniques from Geometric Singular Perturbation Theory (GSPT), and in particular the so-called blow-up method, we desingularize that point and…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…