Exact solution of generalized cooperative SIR dynamics

Abstract

In this paper, we introduce a general framework for co-infection as cooperative SIR dynamics. We first solve analytically CGCG model [1] and then the generalized model in symmetric scenarios. We calculate transition points, order parameter, i.e. total number of infected hosts. Also we show analytically there is a saddle-node bifurcation for two cooperative SIR dynamics and the transition is hybrid. Moreover, we investigate where symmetric solution is stable for initial fluctuations. Then we study asymmetric cases of parameters. The more asymmetry, for the primary and secondary infection rates of one pathogen in comparison to the other pathogen, can lead to the less infected hosts, the higher epidemic threshold and continuous transitions. Our model and results for co-infection in combination with super-infection [2] can open a road to model disease ecology.

References in corpus (16)

• Catastrophic cascade of failures in interdependent networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• Universal behavior in a generalized model of contagion
• Threshold effects for two pathogens spreading on a network
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• A Generalized Epidemic Process and Tricritical Dynamic Percolation
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Outbreaks of coinfections: the critical role of cooperativity
• Fundamental properties of cooperative contagion processes
• Phase Transitions in Cooperative Coinfections: Simulation Results for Networks and Lattices
• Co-circulation of infectious diseases on networks
• First-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process
• Particle velocity controls phase transitions in contagion dynamics
• Modelling Competitive marketing strategies in Social Networks
• Risk of coinfection outbreaks in temporal networks: a case study of a hospital contact network

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• Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics
• Emergence of synergistic and competitive pathogens in a co-evolutionary spreading mode
• Effects of measures on phase transitions in two cooperative susceptible-infectious-recovered dynamics