Related papers: Population extinction in an inhomogeneous host-pat…
Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…
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…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
As pathogens spread in a population of hosts, immunity is built up and the pool of susceptible individuals is depleted. This generates selective pressure, to which many human RNA viruses, such as influenza virus or SARS-CoV-2, respond with…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…
We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…
The dynamic theory of inhomogeneous populations developed during the last decade predicts several essential new dynamic regimes applicable even to the well-known, simple population models. We show that, in an inhomogeneous population with a…
This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system…
Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by $Z_0$ and the size of the $n$th change by $C_n$, $n= 1, 2,…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
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…
Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary…
We introduce and analyze a within-host dynamical model of the coevolution between rapidly mutating pathogens and the adaptive immune response. Pathogen mutation and a homeostatic constraint on lymphocytes both play a role in allowing the…