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Contagious processes on networks, such as spread of disease through physical proximity or information diffusion over social media, are continuous-time processes that depend upon the pattern of interactions between the individuals in the network. Continuous-time stochastic epidemic models are a natural fit for modeling the dynamics of such processes. However, prior work on such continuous-time models doesn’t consider the dynamics of the underlying interaction network which involves addition and removal of edges over time. Instead, researchers have typically simulated these processes using discrete-time approximations, in which one has to trade off between high simulation accuracy and short computation time. In this paper, we incorporate continuous-time network dynamics (addition and removal of edges) into continuous-time epidemic simulations. We propose a rejection-sampling based approach coupled with the well-known Gillespie algorithm that enables exact simulation of the continuous-time epidemic process. Our proposed approach gives exact results, and the computation time required for simulation is reduced as compared to discrete-time approximations of comparable accuracy.
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Continuous Time Graph Processes with Known ERGM Equilibria: Contextual Review, Extensions, and Synthesis
Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case.
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- Award ID(s):
- 1826589
- PAR ID:
- 10392399
- Date Published:
- Journal Name:
- Journal of mathematical sociology
- ISSN:
- 0022-250X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
