Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models
Department of Mathematics, Ariel University, Ariel 40700, Israel
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Academic Editor: Shou-Fu Tian
Symmetry 2021, 13(7), 1120; https://doi.org/10.3390/sym13071120
Received: 27 May 2021
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Revised: 13 June 2021
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Accepted: 15 June 2021
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Published: 23 June 2021
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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 Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale model containing 15 nonlinear ordinary differential equations (ODEs), 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 thanks to the symmetry of the population size over time.
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Keywords:
markov chain; random variable transformation technique; asymptotic stable equilibria state; three age group SIIRD model
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MDPI and ACS Style
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. https://doi.org/10.3390/sym13071120
AMA Style
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(7):1120. https://doi.org/10.3390/sym13071120
Chicago/Turabian StyleLazebnik, Teddy, Svetlana Bunimovich-Mendrazitsky, and Leonid Shaikhet. 2021. "Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models" Symmetry 13, no. 7: 1120. https://doi.org/10.3390/sym13071120
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