Bate, Sara2016-06-212016-06-212015Bate, 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.http://hdl.handle.net/10034/613868The 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.enhttp://creativecommons.org/licenses/by-nc-nd/4.0/Lyapunov methodepidemiologypopulation modelsThesis or dissertation