Time evolution of epidemic disease on finite and infinite networks

Abstract

Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer a new analytical framework, which incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and "infinite"-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology.

17 pages, 7 figures. This version (v4) has been accepted by Physical Review E on December 9, 2008. The first version (v1) of this paper supersedes arXiv:0710.3420 . Version v2, v3 and v4 consist of the first (discrete time) part of v1. It contains a new section IV for comparison with different models. The continuous time part of v1 will appear as a separate contribution

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• Modeling the dynamical interaction between epidemics on overlay networks
• Dynamical Systems on Networks: A Tutorial
• Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
• Untangling the interplay between epidemic spreading and transmission network dynamic
• Vaccination intervention on epidemic dynamics in networks
• Propagation dynamics on networks featuring complex topologies
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• Epidemic fronts in complex networks with metapopulation structure
• Propagation on networks: an exact alternative perspective
• Link-based formalism for time evolution of adaptive networks
• Suppressed epidemics in multi-relational networks
• Predicting the diversity of early epidemic spread on networks
• Early Real-time Estimation of Infectious Disease Reproduction Number
• Absence of epidemic thresholds in a growing adaptive network
• Finite-time scaling for epidemic processes with power-law superspreading events
• The network epidemiology of an Ebola epidemic
• Temporal and probabilistic comparisons of epidemic interventions
• Exact mean field dynamics for epidemic-like processes on heterogeneous networks
• Tracking dynamics of superspreading through contacts, exposures, and transmissions in edge-based network epidemics