Efficient method for comprehensive computation of agent-level epidemic dissemination in networks

Area of Science:

• Epidemiology
• Computational Biology
• Network Science

Background:

• Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) models are fundamental in epidemic studies, simulating disease spread in networks.
• Accurate disease spreading estimation is crucial but often hindered by computationally intensive simulations and limitations of analytical and numerical methods.
• Existing methods face challenges with large populations and complex network structures, restricting precise epidemic analysis.

Purpose of the Study:

• To develop an efficient algebraic method for evaluating stationary states in epidemic Markov processes.
• To overcome the computational limitations of traditional numerical simulations and analytical approaches for disease spreading estimation.
• To leverage network symmetries for a more scalable and accurate analysis of epidemic dynamics.

Main Methods:

• Utilized the squared norm of the probability vector to derive an algebraic equation for stationary states.
• Employed symmetrized time generators and their eigenvalues, reducing the time evolution to an O(N) sparse problem.
• Integrated quantum many-body techniques for eigenvalue calculation and standard perturbation theory for network topology modifications.

Main Results:

• Successfully derived an algebraic equation for evaluating stationary states in epidemic models.
• Reduced the complexity of time evolution analysis from exponential to O(N) by exploiting symmetries.
• Demonstrated a method that is more efficient and scalable for analyzing disease spreading in large networks.

Conclusions:

• The proposed algebraic method offers a significant advancement in the precise and efficient estimation of disease spreading.
• This approach overcomes limitations of traditional methods, enabling analysis of larger and more complex epidemic networks.
• The integration of quantum many-body techniques provides a powerful tool for understanding epidemic dynamics.