A New Perspective on Determining Disease Invasion and Population Persistence in Heterogeneous Environments

TL;DR

This paper introduces the network heterogeneity index, a new mathematical tool that helps analyze disease spread and population survival in complex, heterogeneous environments, with applications in epidemiology and ecology.

Contribution

The paper presents the network heterogeneity index and demonstrates its effectiveness in assessing disease invasion and population persistence in diverse environments.

Findings

The index $\\mathcal{H}$ is non-negative and reflects network structure and dynamics.

The index provides insights into disease invasibility and population persistence.

Applications show the index's usefulness in epidemiology and ecology.

Abstract

We introduce a new quantity known as the network heterogeneity index, denoted by $\mathcal{H}$, which facilitates the investigation of disease propagation and population persistence in heterogeneous environments. Our mathematical analysis reveals that this index embodies the structure of such networks, the disease or population dynamics of patches, and the dispersal between patches. We present multiple representations of the network heterogeneity index and demonstrate that $\mathcal{H}\geq 0$. Moreover, we explore the applications of $\mathcal{H}$ in epidemiology and ecology across various heterogeneous environments, highlighting its effectiveness in determining disease invasibility and population persistence.