Fluctuation effects in metapopulation models: percolation and pandemic threshold.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Metapopulation models are standard for simulating disease spread across connected populations.
• Current models often neglect crucial fluctuations by using mean-field approximations.
• Understanding pandemic spread requires accounting for stochasticity in disease dynamics.

Purpose of the Study:

• To develop and analyze fully stochastic metapopulation models for disease spread.
• To analytically investigate the existence and calculation of global pandemic thresholds.
• To establish a connection between disease spread and network percolation theory.

Main Methods:

• Development of fully stochastic metapopulation models for Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) dynamics.
• Analytical treatment of stochastic models to address disease spread thresholds.
• Mapping the global spread of disease to bond percolation processes on networks.

Main Results:

• Stochastic models allow for analytical solutions regarding disease spread thresholds.
• The global spread of disease is shown to be equivalent to bond percolation on the network.
• An estimate (lower bound) for the pandemic threshold in the SIR model is derived for all parameters and network types.

Conclusions:

• Stochastic metapopulation models offer a more accurate framework for pandemic simulations.
• Network percolation provides a powerful tool for understanding and quantifying pandemic thresholds.
• The findings enable better prediction and management of global disease outbreaks.