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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Public Health

Background:

  • Infectious disease dynamics in enclosed spaces are critical for control.
  • Existing models may not fully capture population flow in and out of systems.

Purpose of the Study:

  • To develop a novel modeling approach for infectious disease dynamics in multi-chamber enclosed spaces.
  • To analyze individual movement and infection status using an open Markov chain framework.

Main Methods:

  • Utilized an open Markov chain framework to model individuals entering/leaving the system.
  • Categorized individuals into susceptible, carrier, and infected states.
  • Employed a discrete-time process to simulate individual behavior and infection dynamics.

Main Results:

  • Derived a probability function to quantify infection risk based on population size and group distribution.
  • Calculated mathematical expressions for average and mean populations of susceptible, carrier, and infected individuals over time.
  • Determined stationary mean populations for each group.

Conclusions:

  • The open Markov chain model provides a robust framework for understanding disease spread in dynamic enclosed environments.
  • The derived mathematical expressions offer valuable tools for risk assessment and public health interventions.
  • Validation through theoretical and numerical comparisons supports the model's efficacy.