Relevance of backtracking paths in epidemic spreading on networks

TL;DR

This paper demonstrates that backtracking paths are crucial in reversible epidemic models on networks, challenging previous assumptions and showing that neglecting them results in inaccurate epidemic threshold predictions.

Contribution

It reveals the importance of backtracking paths in reversible epidemic spreading and introduces a modified model excluding these paths, significantly altering the epidemic dynamics.

Findings

Neglecting backtracking paths leads to incorrect epidemic thresholds.

Forbidding backtracking paths changes the epidemic behavior drastically.

Backtracking paths are essential for accurate modeling of reversible epidemics.

Abstract

The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow to derive exact results for irreversible spreading (i.e. diseases with permanent acquired immunity) in locally-tree like topologies. This success has suggested the application of the same approach to reversible epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e. an individual is reinfected by a neighbor he/she previously infected) do not play a relevant role. In this paper we show that this is not the case for reversible epidemics, since the neglect of backtracking paths leads to a formula for the epidemic threshold that is qualitatively incorrect in the large size limit. Moreover we define a modified reversible dynamics which explicitly forbids direct backtracking events and show that this modification completely upsets the phenomenology.