Heterogeneous mean-field theory for two-species symbiotic processes on networks

Abstract

A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic interaction. The 2SCP is known to exhibit a complex behavior with a rich phase diagram, including continuous and discontinuous transitions between the active phase and extinction. In this work, we advance the understanding of the phase transition of the 2SCP on uncorrelated networks by developing a heterogeneous mean-field (HMF) theory, in which the heterogeneity of contacts is explicitly reckoned. The HMF theory for networks with power-law degree distributions shows that the region of bistability (active and inactive phases) in the phase diagram shrinks as the heterogeneity level is increased by reducing the degree exponent. Finite-size analysis reveals a complex behavior where a pseudo discontinuous transition at a finite-size can be converted into a continuous one in the thermodynamic limit, depending on degree exponent and symbiotic coupling. The theoretical results are supported by extensive numerical simulations.

arXiv commentRevised version with new analytical results; 10 pages, 9 figures

References in corpus (33)

• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Statistical physics of social dynamics
• Epidemic processes in complex networks
• Dynamical interplay between awareness and epidemic spreading in multiplex networks
• Generation of uncorrelated random scale-free networks
• Threshold effects for two pathogens spreading on a network
• Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
• Coevolution spreading in complex networks
• Contact processes on random graphs with power law degree distributions have critical value 0
• Non mean-field behavior of the contact process on scale-free networks
• Suppressing disease spreading by using information diffusion on multiplex networks
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Interacting epidemics and coinfection on contact networks
• Disease Localization in Multilayer Networks
• Outbreaks of coinfections: the critical role of cooperativity
• Heterogeneous pair-approximation for the contact process on complex networks
• Quasi-stationary simulations of the contact process on quenched networks
• Phase Transitions in Cooperative Coinfections: Simulation Results for Networks and Lattices
• Collective versus hub activation of epidemic phases on networks
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Quasi-stationary analysis of the contact process on annealed scale-free networks
• Explosive spreading on complex networks: the role of synergy
• Environmental vs. demographic variability in two-species predator-prey models
• A message-passing approach to epidemic tracing and mitigation with apps
• Rare region effects in the contact process on networks
• First-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process
• Mutually cooperative epidemics on power-law networks
• Phase diagram of the symbiotic two-species contact process
• The symbiotic contact process: phase transitions, hysteresis cycles, and bistability
• Simple quasistationary method for simulations of epidemic processes with localized states
• Role of hubs in the synergistic spread of behavior
• Dynamical correlations and pairwise theory for the symbiotic contact process on networks