Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models
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-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1120 |
| _version_ | 1797529019927756800 |
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| author | Teddy Lazebnik Svetlana Bunimovich-Mendrazitsky Leonid Shaikhet |
| author_facet | Teddy Lazebnik Svetlana Bunimovich-Mendrazitsky Leonid Shaikhet |
| author_sort | Teddy Lazebnik |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T10:07:30Z |
| format | Article |
| id | doaj.art-6873eb3da612481e90384d78711fe418 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:07:30Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6873eb3da612481e90384d78711fe4182023-11-22T01:24:41ZengMDPI AGSymmetry2073-89942021-06-01137112010.3390/sym13071120Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological ModelsTeddy Lazebnik0Svetlana Bunimovich-Mendrazitsky1Leonid Shaikhet2Department of Mathematics, Ariel University, Ariel 40700, IsraelDepartment of Mathematics, Ariel University, Ariel 40700, IsraelDepartment of Mathematics, Ariel University, Ariel 40700, IsraelWe 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.https://www.mdpi.com/2073-8994/13/7/1120markov chainrandom variable transformation techniqueasymptotic stable equilibria statethree age group SIIRD model |
| spellingShingle | Teddy Lazebnik Svetlana Bunimovich-Mendrazitsky Leonid Shaikhet Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models Symmetry markov chain random variable transformation technique asymptotic stable equilibria state three age group SIIRD model |
| title | Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models |
| title_full | Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models |
| title_fullStr | Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models |
| title_full_unstemmed | Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models |
| title_short | Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models |
| title_sort | novel method to analytically obtain the asymptotic stable equilibria states of extended sir type epidemiological models |
| topic | markov chain random variable transformation technique asymptotic stable equilibria state three age group SIIRD model |
| url | https://www.mdpi.com/2073-8994/13/7/1120 |
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