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Non-Markovian edge-based compartmental modeling.

V P Shkilev1

  • 1Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17, General Naumov Str., 03164 Kyiv, Ukraine.

Physical Review. E
|May 22, 2019
PubMed
Summary

This study introduces a novel method to generalize epidemic modeling equations for non-Poissonian processes. The research confirms that complex non-Markovian epidemic models can be simplified into Markovian systems, aiding disease spread analysis.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Compartmental modeling is a key tool for understanding epidemic dynamics.
  • Existing models often assume Poissonian (random) transmission and recovery processes.
  • Non-Poissonian processes, where events are not purely random, present challenges for current models.

Purpose of the Study:

  • To propose a generalized method for edge-based compartmental models.
  • To adapt these models for scenarios with non-Poissonian transmission and recovery.
  • To demonstrate the representation of non-Markovian epidemic systems as Markovian systems.

Main Methods:

  • Development of a novel mathematical framework for generalizing edge-based compartmental models.
  • Application of the proposed method to specific edge-based compartmental model types.

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  • Derivation of analytical expressions for key epidemiological parameters.

    • Main Results:

    • A method is presented to generalize epidemic modeling equations for non-Poissonian processes.
    • Non-Markovian systems describing epidemic spread were successfully represented as Markovian systems.
    • Analytical expressions for the basic reproductive number and final epidemic size were derived for a non-Markovian dynamic variable-degree model.

    Conclusions:

    • The proposed method effectively generalizes compartmental models to non-Poissonian scenarios.
    • The conversion of non-Markovian to Markovian systems simplifies the analysis of epidemic spread.
    • This approach provides valuable tools for deriving epidemiological parameters in complex disease dynamics.