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Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model
The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer India
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7134539/ https://www.ncbi.nlm.nih.gov/pubmed/32289049 http://dx.doi.org/10.1007/s40819-019-0699-7 |
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author | Yaro, David Apeanti, Wilson Osafo Akuamoah, Saviour Worlanyo Lu, Dianchen |
author_facet | Yaro, David Apeanti, Wilson Osafo Akuamoah, Saviour Worlanyo Lu, Dianchen |
author_sort | Yaro, David |
collection | PubMed |
description | The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative is applied to a system of non-integer order differential equation to model the transmission dynamics of respiratory diseases. The nonnegative solutions of the system are obtained by using the Generalized Mean Value Theorem. The next generation matrix approach is used to obtain the basic reproduction number [Formula: see text] . We discuss the stability of the disease-free equilibrium when [Formula: see text] , and the necessary conditions for the stability of the endemic equilibrium when [Formula: see text] . A sensitivity analysis shows that [Formula: see text] is most sensitive to the probability of the disease transmission rate. The results from the numerical simulations of optimal control strategies disclose that the utmost way of controlling or probably eradicating the transmission of respiratory diseases should be quarantining the exposed individuals, monitoring and treating infected people for a substantial period. |
format | Online Article Text |
id | pubmed-7134539 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Springer India |
record_format | MEDLINE/PubMed |
spelling | pubmed-71345392020-04-06 Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model Yaro, David Apeanti, Wilson Osafo Akuamoah, Saviour Worlanyo Lu, Dianchen Int J Appl Comput Math Original Paper The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative is applied to a system of non-integer order differential equation to model the transmission dynamics of respiratory diseases. The nonnegative solutions of the system are obtained by using the Generalized Mean Value Theorem. The next generation matrix approach is used to obtain the basic reproduction number [Formula: see text] . We discuss the stability of the disease-free equilibrium when [Formula: see text] , and the necessary conditions for the stability of the endemic equilibrium when [Formula: see text] . A sensitivity analysis shows that [Formula: see text] is most sensitive to the probability of the disease transmission rate. The results from the numerical simulations of optimal control strategies disclose that the utmost way of controlling or probably eradicating the transmission of respiratory diseases should be quarantining the exposed individuals, monitoring and treating infected people for a substantial period. Springer India 2019-07-15 2019 /pmc/articles/PMC7134539/ /pubmed/32289049 http://dx.doi.org/10.1007/s40819-019-0699-7 Text en © Springer Nature India Private Limited 2019 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 | Original Paper Yaro, David Apeanti, Wilson Osafo Akuamoah, Saviour Worlanyo Lu, Dianchen Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title | Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title_full | Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title_fullStr | Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title_full_unstemmed | Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title_short | Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model |
title_sort | analysis and optimal control of fractional-order transmission of a respiratory epidemic model |
topic | Original Paper |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7134539/ https://www.ncbi.nlm.nih.gov/pubmed/32289049 http://dx.doi.org/10.1007/s40819-019-0699-7 |
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