Application and Optimal Control for an HBV Model with Vaccination and Treatment
In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reprod...
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2018-01-01
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Series: | Discrete Dynamics in Nature and Society |
Online Access: | http://dx.doi.org/10.1155/2018/2076983 |
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doaj-c101c1f09ba44b91af6557ccff2b75982020-11-25T00:04:48ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/20769832076983Application and Optimal Control for an HBV Model with Vaccination and TreatmentJing Zhang0Suxia Zhang1School of Science, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Science, Xi’an University of Technology, Xi’an 710048, ChinaIn this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.http://dx.doi.org/10.1155/2018/2076983 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jing Zhang Suxia Zhang |
spellingShingle |
Jing Zhang Suxia Zhang Application and Optimal Control for an HBV Model with Vaccination and Treatment Discrete Dynamics in Nature and Society |
author_facet |
Jing Zhang Suxia Zhang |
author_sort |
Jing Zhang |
title |
Application and Optimal Control for an HBV Model with Vaccination and Treatment |
title_short |
Application and Optimal Control for an HBV Model with Vaccination and Treatment |
title_full |
Application and Optimal Control for an HBV Model with Vaccination and Treatment |
title_fullStr |
Application and Optimal Control for an HBV Model with Vaccination and Treatment |
title_full_unstemmed |
Application and Optimal Control for an HBV Model with Vaccination and Treatment |
title_sort |
application and optimal control for an hbv model with vaccination and treatment |
publisher |
Hindawi Limited |
series |
Discrete Dynamics in Nature and Society |
issn |
1026-0226 1607-887X |
publishDate |
2018-01-01 |
description |
In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used. |
url |
http://dx.doi.org/10.1155/2018/2076983 |
work_keys_str_mv |
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