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Classification of different Hepatitis B infected individuals with saturated incidence rate
The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new m...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4947085/ https://www.ncbi.nlm.nih.gov/pubmed/27468382 http://dx.doi.org/10.1186/s40064-016-2706-3 |
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author | Khan, Tahir Zaman, Gul |
author_facet | Khan, Tahir Zaman, Gul |
author_sort | Khan, Tahir |
collection | PubMed |
description | The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number [Formula: see text] is investigated by using the well known approach i.e. next generation matrix and investigate the possible equilibriums such as disease free and endemic equilibria. Then for the local and global behavior of the proposed problem, the local asymptotic stability analysis as well as global asymptotic stability analysis are proved. To prove the global asymptotic stability at disease free equilibrium, the classic Lyapunov function theory is considered. Similarly to show global asymptotic stability at endemic equilibria, the geometrical approach is used, which is the generalization of Lyapunov theory. Finally, numeric of the proposed problem are carried out to show the feasibility of the obtained results and the role of saturated incidence rate. |
format | Online Article Text |
id | pubmed-4947085 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-49470852016-07-27 Classification of different Hepatitis B infected individuals with saturated incidence rate Khan, Tahir Zaman, Gul Springerplus Research The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number [Formula: see text] is investigated by using the well known approach i.e. next generation matrix and investigate the possible equilibriums such as disease free and endemic equilibria. Then for the local and global behavior of the proposed problem, the local asymptotic stability analysis as well as global asymptotic stability analysis are proved. To prove the global asymptotic stability at disease free equilibrium, the classic Lyapunov function theory is considered. Similarly to show global asymptotic stability at endemic equilibria, the geometrical approach is used, which is the generalization of Lyapunov theory. Finally, numeric of the proposed problem are carried out to show the feasibility of the obtained results and the role of saturated incidence rate. Springer International Publishing 2016-07-15 /pmc/articles/PMC4947085/ /pubmed/27468382 http://dx.doi.org/10.1186/s40064-016-2706-3 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Khan, Tahir Zaman, Gul Classification of different Hepatitis B infected individuals with saturated incidence rate |
title | Classification of different Hepatitis B infected individuals with saturated incidence rate |
title_full | Classification of different Hepatitis B infected individuals with saturated incidence rate |
title_fullStr | Classification of different Hepatitis B infected individuals with saturated incidence rate |
title_full_unstemmed | Classification of different Hepatitis B infected individuals with saturated incidence rate |
title_short | Classification of different Hepatitis B infected individuals with saturated incidence rate |
title_sort | classification of different hepatitis b infected individuals with saturated incidence rate |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4947085/ https://www.ncbi.nlm.nih.gov/pubmed/27468382 http://dx.doi.org/10.1186/s40064-016-2706-3 |
work_keys_str_mv | AT khantahir classificationofdifferenthepatitisbinfectedindividualswithsaturatedincidencerate AT zamangul classificationofdifferenthepatitisbinfectedindividualswithsaturatedincidencerate |