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Developing a detection model for a COVID-19 infected person based on a probabilistic dynamical system.

Mohamed Abd Allah El-Hadidy1,2

  • 1Mathematics Department, Faculty of Science Tanta University Tanta Egypt.

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|July 7, 2021
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Summary

This study introduces a new model to detect COVID-19 infected individuals in a limited-capacity department using a novel algorithm and Laplace transforms. The model calculates infection detection probabilities over time for improved public health surveillance.

Keywords:
Laplace transformationapplications of queueing theorydynamical systems and their relations with probability theory and stochastic processesprobability of detection

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Queueing Theory

Background:

  • Limited department capacity poses challenges for managing patient flow and infection detection.
  • Accurate real-time assessment of infection probabilities is crucial for effective public health interventions.
  • Existing models may not fully capture the dynamics of patient arrivals, service, and infection spread within a confined setting.

Purpose of the Study:

  • To develop a novel mathematical model for detecting COVID-19 infected individuals in a limited-capacity department.
  • To present an efficient algorithm for calculating the probability of n persons in the department at any time.
  • To determine the detection probability of infected individuals using a specific detection function and steady-state analysis.

Main Methods:

  • Development of a Markovian feedback model considering balking and reneging.
  • Application of a novel algorithm utilizing Laplace transforms to solve a probabilistic dynamical system.
  • Analysis of an exponential detection function and steady-state conditions for probability calculations.

Main Results:

  • An efficient algorithm was presented to calculate the exact probability of n persons in the department.
  • The model provides the detection probability of infected individuals, considering arrival and service dynamics.
  • Numerical examples illustrate the behavior of probabilities and detection rates over time for various capacities.

Conclusions:

  • The proposed model and algorithm offer an effective method for detecting COVID-19 infected persons in limited-capacity environments.
  • The study provides insights into infection dynamics and detection probabilities, valuable for public health planning.
  • The model's flexibility allows for analysis across different department capacities and timeframes.