# Multi-Competitive Viruses over Static and Time--Varying Networks

## TL;DR

This paper studies the spread and control of multiple competing viruses over both static and dynamic networks, extending previous work limited to two viruses and static graphs, and introduces stability analysis and an antidote control method.

## Contribution

It generalizes the analysis of competing viruses to multiple viruses and dynamic networks, providing new stability results and a control strategy.

## Key findings

- Stability conditions for multi-virus systems are derived.
- An antidote control technique is proposed and analyzed.
- The model extends previous two-virus static graph studies.

## Abstract

Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along different social networks. Previous studies of competitive viruses have focused only on two viruses and on static graph structures. In this paper, we consider multiple competing viruses over static and dynamic graph structures, and investigate the eradication and propagation of diseases in these systems. Stability analysis for the class of models we consider is performed and an antidote control technique is proposed.