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Non-Markovian edge-based compartmental modeling

V. P. Shkilev*

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

  • *shkilevv@ukr.net
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Phys. Rev. E 99, 042408 – Published 18 April, 2019

DOI: https://doi.org/10.1103/PhysRevE.99.042408

Abstract

A method is proposed for generalizing the equations obtained within the framework of the edge-based compartmental modeling approach for the case of non-Poissonian transmission and recovery processes. It is confirmed that non-Markovian systems of equations obtained in this manner, which describe the spread of epidemic diseases, can be represented as Markovian systems of equations. The application of the proposed method in particular types of edge-based compartmental models is considered. In particular, the analytical expressions for the basic reproductive number and the final size of an epidemic are derived for the non-Markovian dynamic variable-degree model.

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Outline

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Phys. Rev. E 99, 042408– Published 18 April, 2019
  • Received 17 December 2018
  • Revised 17 March 2019
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