Chaos in a spatial epidemic model

TL;DR

This paper studies a spatial epidemic model inspired by gypsy moth populations, demonstrating chaotic behavior on finite graphs and conjecturing complex oscillations and unique distributions on infinite lattices.

Contribution

It introduces a new spatial epidemic model on various graphs and lattices, proving chaos in finite cases and proposing conjectures for infinite structures.

Findings

Proves convergence to a chaotic dynamical system on finite graphs.

Shows chaotic behavior for certain parameters.

Conjectures about oscillations and stationary distributions on infinite lattices.

Abstract

We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the $d$-dimensional lattice and torus, with $d\geq2$. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjecture that on the infinite lattice with a fixed finite dispersal distance, distant parts of the lattice oscillate out of phase so there is a unique nontrivial stationary distribution.