Some rigorous results for the stacked contact process

TL;DR

This paper rigorously analyzes the phase transition in the stacked contact process, a stochastic model for infection spread among hosts on a lattice, focusing on conditions for infection persistence versus extinction.

Contribution

It provides new rigorous results on the phase transition between infection extinction and persistence in the stacked contact process model.

Findings

Infection persists if the birth rate exceeds a critical threshold.

Extinction occurs when the birth rate is below the critical value.

The model extends the neutral multitype contact process to include vertical and horizontal transmission.

Abstract

The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at the same rate and in accordance to the evolution rules of the neutral multitype contact process. The infection is transmitted both vertically from infected parents to their offspring and horizontally from infected hosts to nearby healthy hosts. The population survives if and only if the common birth rate of healthy and infected hosts exceeds the critical value of the basic contact process. The main purpose of this work is to study the existence of a phase transition between extinction and persistence of the infection in the parameter region where the hosts survive.