Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

Subject Areas

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

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