The Application of Lyapunov Method for the Investigation of Global Stability of Some Population and Epidemiology Models

Hdl Handle:
http://hdl.handle.net/10034/613868
Title:
The Application of Lyapunov Method for the Investigation of Global Stability of Some Population and Epidemiology Models
Authors:
Bate, Sara
Abstract:
The primary purpose of this thesis is to determine the global behaviour of some population and epidemiology models through the application of Lyapunov functions. Using Lyapunov functions and applying these to mathematical models of ODE systems representing different predator-prey models, we were able to determine global assymptotic stability for their equilibrium points. Similarly, for the investigation into the stability of epidemiological models, we were able to analyse various SIRS, SIR, SIS and SEIR models to also conclude global assymptotic stability by implementing the Lyapunov direct method. We then continue our investigation by the application of Lyapunov functions to PDE systems representing reaction-diffusion systems of various predator-prey and epidemiological models. We have also been able to conclude global assymptotic stability for their corresponding equilibriums in these cases. We then proceeded to create our own reaction-diffusion system from a previously constructed ODE system and have been able to prove that for both cases they have a globally assymptotically stable endemic equilibrium.
Citation:
Bate, S. (2015). The application of lyapunov method for the investigation of global stability of some population and epidemiology models. (Master's thesis). University of Chester, United Kingdom.
Publisher:
University of Chester
Publication Date:
2015
URI:
http://hdl.handle.net/10034/613868
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.authorBate, Saraen
dc.date.accessioned2016-06-21T12:02:07Zen
dc.date.available2016-06-21T12:02:07Zen
dc.date.issued2015en
dc.identifier.citationBate, S. (2015). The application of lyapunov method for the investigation of global stability of some population and epidemiology models. (Master's thesis). University of Chester, United Kingdom.en
dc.identifier.urihttp://hdl.handle.net/10034/613868en
dc.description.abstractThe primary purpose of this thesis is to determine the global behaviour of some population and epidemiology models through the application of Lyapunov functions. Using Lyapunov functions and applying these to mathematical models of ODE systems representing different predator-prey models, we were able to determine global assymptotic stability for their equilibrium points. Similarly, for the investigation into the stability of epidemiological models, we were able to analyse various SIRS, SIR, SIS and SEIR models to also conclude global assymptotic stability by implementing the Lyapunov direct method. We then continue our investigation by the application of Lyapunov functions to PDE systems representing reaction-diffusion systems of various predator-prey and epidemiological models. We have also been able to conclude global assymptotic stability for their corresponding equilibriums in these cases. We then proceeded to create our own reaction-diffusion system from a previously constructed ODE system and have been able to prove that for both cases they have a globally assymptotically stable endemic equilibrium.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectLyapunov methoden
dc.subjectepidemiologyen
dc.subjectpopulation modelsen
dc.titleThe Application of Lyapunov Method for the Investigation of Global Stability of Some Population and Epidemiology Modelsen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
dc.description.advisorKavallaris, Nikosen
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