A Model for the Multi-Virus Contact Process

TL;DR

This paper analyzes a multi-virus contact process on graphs, showing that on finite graphs the process almost surely dies out for any positive infection rate, and providing bounds for survival on infinite regular trees.

Contribution

It introduces a multi-virus contact process model with node removal based on infection count and establishes extinction results on finite graphs and bounds for survival on infinite trees.

Findings

Process dies out almost surely on finite graphs for any positive infection rate

Provides lower bounds for infection rate for survival on infinite regular trees

Provides upper bounds for infection rate leading to die out on infinite trees

Abstract

We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of infections the node carries at the moment when it gets another infection. In this paper, we show that on any finite graph, any positive value of infection rate $\lambda$ will result in the death of the process almost surely. In the case of $d$-regular infinite trees, We also give a lower bound on the infection rate in order for the process to survive, and an upper bound for the process to die out.