Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment

An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below...

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Main Authors: Yakui Xue, Junfeng Wang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/647853
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author Yakui Xue
Junfeng Wang
author_facet Yakui Xue
Junfeng Wang
author_sort Yakui Xue
collection DOAJ
description An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
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publishDate 2012-01-01
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spelling doaj-art-5c9a413ecacc46e88ddf5bed69adff892025-08-20T02:04:59ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/647853647853Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and TreatmentYakui Xue0Junfeng Wang1Department of Mathematics, North University of China, Shanxi Taiyuan 030051, ChinaDepartment of Mathematics, North University of China, Shanxi Taiyuan 030051, ChinaAn epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.http://dx.doi.org/10.1155/2012/647853
spellingShingle Yakui Xue
Junfeng Wang
Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
Abstract and Applied Analysis
title Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
title_full Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
title_fullStr Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
title_full_unstemmed Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
title_short Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
title_sort backward bifurcation of an epidemic model with infectious force in infected and immune period and treatment
url http://dx.doi.org/10.1155/2012/647853
work_keys_str_mv AT yakuixue backwardbifurcationofanepidemicmodelwithinfectiousforceininfectedandimmuneperiodandtreatment
AT junfengwang backwardbifurcationofanepidemicmodelwithinfectiousforceininfectedandimmuneperiodandtreatment