Coexistence in a two-type continuum growth model

TL;DR

This paper introduces a stochastic model for two competing infections spreading on Euclidean space, demonstrating that equal infection intensities can lead to simultaneous unbounded growth of both types.

Contribution

It presents a new continuum growth model with spherical outbursts for competing infections and proves the possibility of coexistence when infection intensities are equal.

Findings

Equal infection intensities allow for positive probability of coexistence.

Both infection types can grow unboundedly simultaneously.

The model captures stochastic growth dynamics in continuous space.

Abstract

We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all previously uninfected points within a stochastic distance from the outburst location to be type 1 (2) infected. The main result is that, if the infection types have the same intensity, then there is a strictly positive probability that both infection types grow unboundedly.