Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-type Epidemiological Models

Version 1 : Received: 25 May 2021 / Approved: 26 May 2021 / Online: 26 May 2021 (14:29:42 CEST)

A peer-reviewed article of this Preprint also exists.

Lazebnik, T.; Bunimovich-Mendrazitsky, S.; Shaikhet, L. Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models. Symmetry 2021, 13, 1120. Lazebnik, T.; Bunimovich-Mendrazitsky, S.; Shaikhet, L. Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models. Symmetry 2021, 13, 1120.

Journal reference: Symmetry 2021, 13, 1120
DOI: 10.3390/sym13071120

Abstract

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the SIR-type epidemiological model that we developed for viral diseases with long-term immunity memory pandemic. This is a large-scale model containing 15 nonlinear ODE equations, and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions.

Keywords

Markov chain; random variable transformation technique; asymptotic stable equilibria state; three age group SIIRD model

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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