Efficient and Realistic Stochastic Simulation of the Dynamics of Epidemic Processes on Complex Networks

This article investigates the impact of the structure of the contact network on the dynamics of epidemic outbreaks, particularly focusing on the peak count of infected nodes (PCIN). The height of the PCIN is crucial in determining the maximum operational capacity of intensive care units (ICUs). Postponing the peak infection count is vital to ensure the preparedness of the ICUs. To facilitate this objective, we have developed an open-source Python-based analytical dashboard. This dashboard uses a continuous-time Markov chain model (CTMC model) that provides a realistic prediction of the dynamic behavior of the epidemic process given the structure of the contact network and infection rates.To make stochastic simulations scalable, we introduce a fast simulation technique. Our method is based on an adaptation of Gillespie's Stochastic Simulation Algorithm, and it is specifically exploiting the sparseness of the state-transition matrix. This approach effectively counters the exponential increase in population-based state spaces, which typically arises from a conventional implementation of Gillespie's algorithm, especially as the number of nodes escalates. Additionally, the dashboard is capable of simulating stochastic trajectories of an epidemic across various network topologies and identifying, as well as graphically illustrating, prevalent infection pathways of the virus propagation. Employing the dashboard simulations, we conduct an analysis of how network topology influences outbreak dynamics and the PCIN. This analysis is performed using random graph models that represent various complex network topologies. These include Erdős-Rényi, Watts-Strogatz, Barabási-Albert and complete graph (clique) models, with node counts ranging from 500 to 10,000. We graphically represent infection pathways and scrutinize interpretable graph characteristics, such as average path length and clustering coefficient. These features help to systematically understand the influence of network topology on the PCIN. The findings of this study offer valuable information and could guide the development of precise intervention strategies for effective outbreak management.