Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Khan, Tahir, Zaman, Gul
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
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
_version_ 1782443105166819328
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