# Stability of Piecewise Deterministic Markovian Metapopulation Processes on Networks

## TL;DR

This paper analyzes the stability and long-term behavior of a Markovian metapopulation model on networks, providing conditions for stability, boundedness, and ergodicity under different transfer dynamics.

## Contribution

It introduces new stability criteria for a class of Markovian metapopulation models on directed graphs with deterministic intra-node dynamics.

## Key findings

- Derived stability conditions for models with constant jump rates.
- Established criteria for boundedness and ergodicity.
- Provided general conditions for model stability and long-term behavior.

## Abstract

The purpose of this paper is to study a Markovian metapopulation model on a directed graph with edge-supported transfers and deterministic intra-nodal population dynamics. We first state tractable stability conditions for two typical frameworks motivated by applications: constant jump rates with multiplicative transfer amplitudes, and coercive jump rates with unitary transfers. More general criteria for boundedness, petiteness and ergodicity are then given.