Multi-state epidemic processes on complex networks

TL;DR

This paper analyzes multi-state epidemic models on complex networks, revealing how heterogeneity influences epidemic thresholds and pathogen coexistence, with implications for understanding disease dynamics and control strategies.

Contribution

It provides a comprehensive analysis of steady states in multi-state epidemic models on complex networks, highlighting the effects of heterogeneity and competition among pathogens.

Findings

Heterogeneity generally lowers epidemic thresholds.

Coexistence of pathogens depends on network-independent conditions.

Models without spontaneous transitions are unaffected by heterogeneity.

Abstract

Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks underlying infection events are often much more complex than described by meanfield equations or regular lattices. In models with simple transition rules such as the SIS and SIR models, heterogeneous contact rates are known to decrease epidemic thresholds. We analyze steady states of various multi-state disease propagation models with heterogeneous contact rates. In many models, heterogeneity simply decreases epidemic thresholds. However, in models with competing pathogens and mutation, coexistence of different pathogens for small infection rates requires network-independent conditions in addition to heterogeneity in contact rates. Furthermore, models without spontaneous neighbor-independent state transitions, such as cyclically competing species, do not show heterogeneity effects.