The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact

The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact

We propose a novel SIR epidemic dynamical control model with media impact, where the state dependent pulse vaccination and medication treatment control strategies are being introduced to prevent the spread of disease at different control threshold values. By using the geometry theory of differential...

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Main Authors: Zhi-Long He, Lin-Fei Nie
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/532494
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spelling doaj-a347050756f1469ea0446fca6856a38d2020-11-24T22:34:32ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/532494532494The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media ImpactZhi-Long He0Lin-Fei Nie1College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaWe propose a novel SIR epidemic dynamical control model with media impact, where the state dependent pulse vaccination and medication treatment control strategies are being introduced to prevent the spread of disease at different control threshold values. By using the geometry theory of differential equation and method of successor function, the existence of positive order-1 periodic solution is studied. Further, some sufficient conditions of the orbitally asymptotical stability for positive order-1 periodic solution are given by the analog Poincaré criterion. Furthermore, numerical simulations are carried to illustrate the feasibility of our main results presented here.http://dx.doi.org/10.1155/2015/532494
collection DOAJ
language English
format Article
sources DOAJ
author Zhi-Long He
Lin-Fei Nie
spellingShingle Zhi-Long He
Lin-Fei Nie
The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
Discrete Dynamics in Nature and Society
author_facet Zhi-Long He
Lin-Fei Nie
author_sort Zhi-Long He
title The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
title_short The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
title_full The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
title_fullStr The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
title_full_unstemmed The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact
title_sort effect of pulse vaccination and treatment on sir epidemic model with media impact
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2015-01-01
description We propose a novel SIR epidemic dynamical control model with media impact, where the state dependent pulse vaccination and medication treatment control strategies are being introduced to prevent the spread of disease at different control threshold values. By using the geometry theory of differential equation and method of successor function, the existence of positive order-1 periodic solution is studied. Further, some sufficient conditions of the orbitally asymptotical stability for positive order-1 periodic solution are given by the analog Poincaré criterion. Furthermore, numerical simulations are carried to illustrate the feasibility of our main results presented here.
url http://dx.doi.org/10.1155/2015/532494
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AT zhilonghe effectofpulsevaccinationandtreatmentonsirepidemicmodelwithmediaimpact
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