Related papers: First-passage competition with different speeds: p…
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the…
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,…
We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of…
Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of…
In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible…
The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms through which extinction of infection propagation comes about. We here report on a…
The epidemic process on a graph is considered for which infectious contacts occur at rate which depends on whether a susceptible is infected for the first time or not. We show that the Vasershtein coupling extends if and only if secondary…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
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…
In this paper we consider a competition system in which two diseases spread by contact. We characterize the system behavior, establishing that only some configurations are possible. In particular we discover that coexistence of the two…
Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at…
We investigate a model of a parasite population invading spatially distributed immobile hosts on a graph, which is a modification of the frog model. Each host has an unbreakable immunity against infection with a certain probability $1-p$…
We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field…
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…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state…
We show that a bacteria and bacteriophage system with either a perfectly nested or a one-to-one infection network is permanent, a.k.a uniformly persistent, provided that bacteria that are superior competitors for nutrient devote the least…
This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…
We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1…
We investigate the full temporal evolution of epidemic outbreaks in complex networks, focusing on the susceptible-infected (SI) model of disease transmission. Combining theoretical analysis with large-scale numerical simulations, we uncover…