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An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness
In this work, we propose a nonlinear susceptible (S), vaccinated (V), infective (I), recovered (R), information level (U) (SVIRUS) model for the dynamical behavior of the contagious disease in human beings. We mainly consider the spread of information during the course of epidemic in the population....
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8423856/ https://www.ncbi.nlm.nih.gov/pubmed/34514081 http://dx.doi.org/10.1007/s40808-021-01257-7 |
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author | Mahato, Prasenjit Das, Subhashis Mahato, Sanat Kumar |
author_facet | Mahato, Prasenjit Das, Subhashis Mahato, Sanat Kumar |
author_sort | Mahato, Prasenjit |
collection | PubMed |
description | In this work, we propose a nonlinear susceptible (S), vaccinated (V), infective (I), recovered (R), information level (U) (SVIRUS) model for the dynamical behavior of the contagious disease in human beings. We mainly consider the spread of information during the course of epidemic in the population. Different rate equations describe the dynamics of the information. We have developed the proposed model in crisp and fuzzy environments. In the fuzzy model, to describe the uncertainty prevailed in the dynamics, all the parameters are taken as triangular fuzzy numbers. Using graded mean integration value (GMIV) method, the fuzzy model is transformed into defuzzified model to represent the solutions avoiding the difficulties. The positivity and the boundedness of the crisp model are discussed elaborately and also the equilibrium analysis is accomplished. The stability analysis for both the infection free and the infected equilibrium are established for the crisp model. Application of optimal control of the crisp system is explored. Using Pontryagin’s Maximum Principle, the optimal control is explained. The effect of vaccination is analyzed which leads the model to be complex in nature. The effect of saturation constant for information is described for the crisp model and also the effects of weight constants on control policy are discussed. Finally, it is concluded that the treatment is more fruitful and information related vaccination is more effective during the course of epidemic. |
format | Online Article Text |
id | pubmed-8423856 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-84238562021-09-08 An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness Mahato, Prasenjit Das, Subhashis Mahato, Sanat Kumar Model Earth Syst Environ Review Article In this work, we propose a nonlinear susceptible (S), vaccinated (V), infective (I), recovered (R), information level (U) (SVIRUS) model for the dynamical behavior of the contagious disease in human beings. We mainly consider the spread of information during the course of epidemic in the population. Different rate equations describe the dynamics of the information. We have developed the proposed model in crisp and fuzzy environments. In the fuzzy model, to describe the uncertainty prevailed in the dynamics, all the parameters are taken as triangular fuzzy numbers. Using graded mean integration value (GMIV) method, the fuzzy model is transformed into defuzzified model to represent the solutions avoiding the difficulties. The positivity and the boundedness of the crisp model are discussed elaborately and also the equilibrium analysis is accomplished. The stability analysis for both the infection free and the infected equilibrium are established for the crisp model. Application of optimal control of the crisp system is explored. Using Pontryagin’s Maximum Principle, the optimal control is explained. The effect of vaccination is analyzed which leads the model to be complex in nature. The effect of saturation constant for information is described for the crisp model and also the effects of weight constants on control policy are discussed. Finally, it is concluded that the treatment is more fruitful and information related vaccination is more effective during the course of epidemic. Springer International Publishing 2021-09-08 2022 /pmc/articles/PMC8423856/ /pubmed/34514081 http://dx.doi.org/10.1007/s40808-021-01257-7 Text en © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Review Article Mahato, Prasenjit Das, Subhashis Mahato, Sanat Kumar An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title | An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title_full | An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title_fullStr | An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title_full_unstemmed | An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title_short | An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
title_sort | epidemic model through information-induced vaccination and treatment under fuzzy impreciseness |
topic | Review Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8423856/ https://www.ncbi.nlm.nih.gov/pubmed/34514081 http://dx.doi.org/10.1007/s40808-021-01257-7 |
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