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We developed a method to calculate the probability of extensive epidemic outbreaks, like COVID-19, in large populations using stochastic models. This approach accurately predicts both common and extreme outbreak scenarios, offering new insights into epidemic dynamics.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Statistical Physics

Background:

  • Recent epidemic outbreaks, such as COVID-19, highlight the need for robust models to predict disease spread.
  • Stochastic epidemic models with demographic noise are crucial for understanding population-level disease dynamics.
  • Calculating the likelihood of extensive outbreaks, especially extreme ones, remains a significant challenge.

Purpose of the Study:

  • To develop a general method for calculating the dynamics and likelihood of extensive outbreaks in large populations.
  • To analyze the probability distribution of all extensive outbreaks, including extreme proportions of infected individuals.
  • To provide a theoretical framework applicable to various stochastic epidemic models, including the susceptible-infected-recovered (SIR) model.

Main Methods:

  • Utilizing a large population limit approximation for stochastic epidemic models.
  • Computing the probability distribution of extensive outbreaks.
  • Analyzing the statistical properties of rare events in discrete-state stochastic systems.

Main Results:

  • A method to compute the probability distribution for all extensive outbreaks in large populations.
  • Demonstration that the statistics of extreme outbreaks arise from a continuum of Hamiltonian paths.
  • Identification of unique boundary conditions and conserved probability flux associated with these extreme events.

Conclusions:

  • The developed approach provides a comprehensive framework for understanding epidemic outbreak probabilities, including rare extreme events.
  • The findings offer new insights into the statistical mechanics of epidemic dynamics and rare event statistics.
  • This work has implications for public health preparedness and response strategies for infectious diseases.