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We analyzed how noise causes epidemics to end on complex networks. Our findings predict disease extinction paths and times, validated by simulations on various network types.

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Area of Science:

  • Epidemiology
  • Network Science
  • Statistical Physics

Background:

  • Long-lived epidemics on complex networks are a significant public health concern.
  • Understanding disease extinction dynamics is crucial for effective intervention strategies.
  • Intrinsic noise plays a critical role in epidemic fade-out.

Purpose of the Study:

  • To analytically study epidemic extinction on finite complex networks driven by intrinsic noise.
  • To predict key extinction dynamics: large fluctuation distributions, optimal extinction paths, and average extinction times.
  • To validate predictions using simulations on diverse synthetic and empirical networks.

Main Methods:

  • Application of analytical techniques to the stochastic susceptible-infected-susceptible (SIS) model.
  • Development of methods to predict fluctuation distributions and optimal paths in general network configurations.
  • Utilizing Monte Carlo simulations for validation.

Main Results:

  • Accurate prediction of epidemic extinction dynamics, including large fluctuations and optimal paths.
  • Validation of analytical predictions against simulations on synthetic (weighted, degree-distributed, correlated) and empirical (high school contact) networks.
  • Quantification of scaling patterns for optimal paths and fluctuation distributions in networks with heterogeneous centrality and degree distributions.

Conclusions:

  • The analytical approach effectively models and predicts epidemic extinction in complex networks.
  • Intrinsic noise significantly influences epidemic fade-out dynamics and network structure impacts these processes.
  • The study provides a framework for understanding disease-free transitions in realistic network environments.