Related papers: Rare Event Extinction on Stochastic Networks
Recent work of M.D. Johnston et al. has produced sufficient conditions on the structure of a chemical reaction network which guarantee that the corresponding discrete state space system exhibits an extinction event. The conditions consist…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
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…
Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact…
In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network…
The manner epidemics occurs in a social network depends on various elements, with two of the most influential being the relationships among individuals in the population and the mechanism of transmission. In this paper, we assume that the…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…
Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-year life cycle and is endowed with a high survival…
We give an explicit formula for the most likely path to extinction for the Galton-Watson processes with large initial population. We establish this result with the help of the large deviation principle (LDP) which also recovers the…
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…
We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations formulated in terms of an optimal escape path. We find that different random vaccination strategies can have widely…
In dense Erd\H{o}s-R\'enyi random graphs, we are interested in the events where large numbers of a given subgraph occur. The mean behavior of subgraph counts is known, and only recently were the related large deviations results discovered.…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on random networks. By studying temporal evolution 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…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…