Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks

Abstract

The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations coming from that if one node is occupied, or infected (for disease spreading models), then its neighbors are likely to be occupied. By combining two theoretical approaches---the heterogeneous mean-field theory and the effective degree method---we are able to include these correlations in an analytical solution of the SIS model. We derive accurate expressions for the average prevalence (fraction of infected) and epidemic threshold. We also discuss how to generalize the approach to a larger class of stochastic population models.

24 pages, many figure. Some relevant notes and remarks are added

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• Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks
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• Quenched mean-field theory for the majority-vote model on complex networks
• Logistic growth on networks: exact solutions for the SI model
• Coexistence of positive and negative information in information-epidemic dynamics on multiplex networks
• Multistage onset of epidemics in heterogeneous networks
• The universality of physical images at relative timescales on multiplex networks
• Correlation between transition probability and network structure in epidemic model
• Hierarchical Coarse-grained Approach to the Duration-dependent Spreading Dynamics in Complex Networks
• The effect of role-based resource allocation on epidemic dynamics