Relevance of backtracking paths in epidemic spreading on networks

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.

7 pages, 8 figures

References in corpus (11)

• Critical phenomena in complex networks
• Thresholds for epidemic spreading in networks
• A message passing approach for general epidemic models
• Percolation on sparse networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Predicting percolation thresholds in networks
• Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
• Eigenvector localization in real networks and its implications for epidemic spreading
• Breaking of the site-bond percolation universality in networks
• The lifespan method as a tool to study criticality in absorbing-state phase transitions

Cited by in corpus (8)

• Non massive immunization to contain spreading on complex networks
• Percolation and the effective structure of complex networks
• Node Immunization with Non-backtracking Eigenvalues
• Spectral theory of the non-backtracking Laplacian for graphs
• The matrix product approximation for the dynamic cavity method
• Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix
• Comparison of theoretical approaches for epidemic processes with waning immunity in complex networks
• The Perron non-backtracking eigenvalue after node addition