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PHENOMENOLOGICAL STUDY OF BACKWARD BIFURCATION IN EPIDEMIOLOGICAL MODELS

Byron Manuhwa

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Abstract

This thesis is about the phenomenological study of bifurcations in epidemiologicalmodels, in particular, in backward bifurcation. We consider models that exhibit such bifurcation and also consider the factors that cause them. In order to make the reader understand backward bifurcation, we frst consider transcritical bifurcation and show how it is related to backward bifurcation. We consider our own examples to show these bifurcations and strengthen the cases of occurrence of such bifurcation for certain range of parameters.

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What this paper is about

This thesis is about the phenomenological study of bifurcations in epidemiologicalmodels, in particular, in backward bifurcation. We consider models that exhibit such bifurcation and also consider the factors that cause them. In order to make the reader understand backward bifurcation, we frst consider transcritical bifurcation and show how it is related to backward bifurcation. We consider our own examples to show these bifurcations and strengthen the cases of occurrence of such bifurcation for certain range of parameters.

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Available abstract

This thesis is about the phenomenological study of bifurcations in epidemiologicalmodels, in particular, in backward bifurcation. We consider models that exhibit such bifurcation and also consider the factors that cause them. In order to make the reader understand backward bifurcation, we frst consider transcritical bifurcation and show how it is related to backward bifurcation. We consider our own examples to show these bifurcations and strengthen the cases of occurrence of such bifurcation for certain range of parameters.

Key concepts: Transcritical bifurcation, Bifurcation, Saddle-node bifurcation, Biological applications of bifurcation theory, Bogdanov–Takens bifurcation, Bifurcation diagram, Mathematics, Homoclinic bifurcation

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