Convergence rates for subcritical threshold-one contact processes on lattices

TL;DR

This paper investigates the exponential convergence to zero of infection probability in subcritical threshold-one contact processes on lattices, providing a limit theorem as lattice degree increases, applicable also to classic contact processes.

Contribution

It establishes the exponential decay rate and its limit behavior for contact processes on lattices, extending to classic models.

Findings

Infection probability converges to zero exponentially in subcritical cases.

The exponential rate I has a well-defined limit as lattice degree grows.

Results apply to both threshold-one and classic contact processes.

Abstract

In this paper we are concerned with threshold-one contact processes on lattices. We show that the probability that the origin is infected converges to 0 at an exponential rate I in the subcritical case. Furthermore, we give a limit theorem for I as the degree of the lattice grows to infinity. Our results also hold for classic contact processes on lattices.