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Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

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A new temporal Gillespie algorithm enables faster, exact simulations of dynamic processes on temporal networks. This method significantly outperforms traditional rejection sampling for complex network analysis and epidemic modeling.

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Area of Science:

  • Complex Systems Science
  • Computational Science
  • Network Science

Background:

  • Stochastic simulations are crucial for analyzing dynamical processes on complex networks.
  • Fast algorithms are essential for large-scale simulations.
  • Adapting the Gillespie algorithm to temporal networks presents significant challenges.

Purpose of the Study:

  • To present a novel temporal Gillespie algorithm for simulating stochastic processes on temporal networks.
  • To enable faster and stochastically exact simulations compared to existing methods.
  • To extend the algorithm for non-Markovian processes and demonstrate its application in epidemic modeling.

Main Methods:

  • Developed a temporal Gillespie algorithm applicable to general Poisson processes on temporal networks.
  • Extended the algorithm to handle non-Markovian processes.
  • Provided pseudocode and C++ implementation for epidemic models (SIS, SIR).

Main Results:

  • The temporal Gillespie algorithm is stochastically exact.
  • Achieved speedups of multiple orders of magnitude compared to rejection sampling.
  • Demonstrated 10 to 100 times faster simulations on empirical networks.

Conclusions:

  • The temporal Gillespie algorithm offers a significant advancement for simulating dynamical processes on temporal networks.
  • The method is efficient, exact, and versatile, applicable to both Markovian and non-Markovian processes.
  • Facilitates practical, large-scale simulations for network dynamics and epidemic modeling.