Simulating epidemic peak dynamics on complex networks using efficient Gillespie algorithms.

Area of Science:

• Epidemiology
• Network Science
• Computational Biology

Background:

• Understanding epidemic spreading on complex networks is crucial for public health.
• Network structure and interventions significantly influence epidemic dynamics.
• Existing simulation methods can be computationally intensive.

Purpose of the Study:

• To investigate how network topology and targeted interventions affect epidemic peak count and timing.
• To provide an open-source dashboard for interactive exploration of epidemic models.
• To develop a high-performance simulation engine for epidemic spreading.

Main Methods:

• Analysis of continuous-time SI/SIS/SIR dynamics with edge-specific infection rate reduction and node-level recovery acceleration.
• Development of an extended dashboard simulator with features like non-exponential recovery times and temporal rewiring.
• Redesign of Gillespie's algorithm for sparse graphs, optimizing transition rate updates and node list management.

Main Results:

• Explicit bounds on peak height and delay were derived for heterogeneous network topologies.
• The redesigned Gillespie's algorithm offers multiplicative speed increases over state-of-the-art sparse network implementations.
• Benchmarks on Barabási-Albert networks demonstrated order-of-magnitude performance gains.

Conclusions:

• Network structure and interventions are key determinants of epidemic spread characteristics.
• The developed simulation engine and dashboard provide powerful tools for epidemic research.
• The optimized algorithm significantly enhances the efficiency of simulating epidemic dynamics on large, sparse networks.