Global stability of SIR models with nonlinear incidence and discontinuous treatment

In this article, we study an SIR model with nonlinear incidence rate. By defining the Filippov solution for the model and constructing suitable Lyapunov functions, we show that the global dynamics are fully determined by the basic reproduction number $R_0$, under certain conditions on the incide...

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Main Authors:	Mei Yang, Fuqin Sun
Format:	Article
Language:	English
Published:	Texas State University 2015-12-01
Series:	Electronic Journal of Differential Equations
Subjects:	Filippov solution discontinuous treatment reproduction number asymptotic stability
Online Access:	http://ejde.math.txstate.edu/Volumes/2015/304/abstr.html

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spelling	doaj-9fedba9e939e4120b4246f5a52fa18742020-11-24T22:57:37ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-12-012015304,18Global stability of SIR models with nonlinear incidence and discontinuous treatmentMei Yang0Fuqin Sun1 Tianjin Univ. of Technology and Education, China Tianjin Univ. of Technology and Education, China In this article, we study an SIR model with nonlinear incidence rate. By defining the Filippov solution for the model and constructing suitable Lyapunov functions, we show that the global dynamics are fully determined by the basic reproduction number $R_0$, under certain conditions on the incidence rate and treatment functions. When $R_0\leq 1$ the disease-free equilibrium is globally asymptotically stable, and when $R_0>1$ the unique endemic equilibrium is globally asymptotically stable.http://ejde.math.txstate.edu/Volumes/2015/304/abstr.htmlFilippov solutiondiscontinuous treatmentreproduction numberasymptotic stability
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mei Yang Fuqin Sun
spellingShingle	Mei Yang Fuqin Sun Global stability of SIR models with nonlinear incidence and discontinuous treatment Electronic Journal of Differential Equations Filippov solution discontinuous treatment reproduction number asymptotic stability
author_facet	Mei Yang Fuqin Sun
author_sort	Mei Yang
title	Global stability of SIR models with nonlinear incidence and discontinuous treatment
title_short	Global stability of SIR models with nonlinear incidence and discontinuous treatment
title_full	Global stability of SIR models with nonlinear incidence and discontinuous treatment
title_fullStr	Global stability of SIR models with nonlinear incidence and discontinuous treatment
title_full_unstemmed	Global stability of SIR models with nonlinear incidence and discontinuous treatment
title_sort	global stability of sir models with nonlinear incidence and discontinuous treatment
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2015-12-01
description	In this article, we study an SIR model with nonlinear incidence rate. By defining the Filippov solution for the model and constructing suitable Lyapunov functions, we show that the global dynamics are fully determined by the basic reproduction number $R_0$, under certain conditions on the incidence rate and treatment functions. When $R_0\leq 1$ the disease-free equilibrium is globally asymptotically stable, and when $R_0>1$ the unique endemic equilibrium is globally asymptotically stable.
topic	Filippov solution discontinuous treatment reproduction number asymptotic stability
url	http://ejde.math.txstate.edu/Volumes/2015/304/abstr.html
work_keys_str_mv	AT meiyang globalstabilityofsirmodelswithnonlinearincidenceanddiscontinuoustreatment AT fuqinsun globalstabilityofsirmodelswithnonlinearincidenceanddiscontinuoustreatment
_version_	1725650049424162816

Global stability of SIR models with nonlinear incidence and discontinuous treatment

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