Related papers: A stochastic model for competing growth on $\mathb…

We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…

We study a large family of competing spatial growth models. In these the vertices in Z^d can take on three possible states {0,1,2}. Vertices in states 1 and 2 remain in their states forever, while vertices in state 0 which are adjacent to a…

We study a random growth model on $\R^d$ introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim at finding conditions…

We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected region when infected and susceptible…

We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem.…

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 two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for…

The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…

This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…

We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…

In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that…

We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…

Consider two epidemics whose expansions on $\mathbb{Z}^d$ are governed by two families of passage times that are distinct and stochastically comparable. We prove that when the weak infection survives, the space occupied by the strong one is…

We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field…

We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…

A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…

We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization…