Heterogeneity in susceptible-infected-removed (SIR) epidemics on lattices

Area of Science:

• Epidemiology
• Mathematical modeling
• Statistical physics

Background:

• The percolation paradigm is crucial for understanding disease spread in spatially explicit models, effectively identifying epidemic thresholds in homogeneous systems.
• However, its predictive power diminishes in heterogeneous environments, where epidemic thresholds are difficult to determine without simulations.

Purpose of the Study:

• To analyze the impact of heterogeneity in transmissibility on epidemic invasion thresholds within a stochastic susceptible-infected-removed model.
• To extend the percolation paradigm to accurately model disease dynamics in heterogeneous environments.

Main Methods:

• A stochastic susceptible-infected-removed epidemic model was implemented on a two-dimensional lattice.
• Transmissibility was treated as a random variable drawn from a probability distribution to introduce heterogeneity.
• A two-dimensional phase diagram was analyzed to delineate invasive and non-invasive regimes based on transmissibility parameters.

Main Results:

• The resilience of epidemic systems to invasion is governed by the mean and variance of transmissibility.
• A phase boundary was identified in the mean-variance parameter space, separating invasive (high mean, low variance) from non-invasive (low mean, high variance) regions.
• The percolation paradigm was successfully extended to account for heterogeneity in transmissibility.

Conclusions:

• Heterogeneity in transmissibility can be effectively managed using mean and variance as control parameters.
• The findings provide a framework for analyzing disease control strategies in realistic, heterogeneous epidemic systems.
• This research bridges the gap between theoretical percolation models and complex real-world disease dynamics.