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Theses and Dissertations

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Browsing Theses and Dissertations by Author "Antolin, Michael, committee member"

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    Bifurcation of semialgebraic maps
    (Colorado State University. Libraries, 2014) Drendel, Jesse William, author; Bates, Daniel, advisor; Shipman, Patrick, advisor; Tavener, Simon, committee member; Antolin, Michael, committee member
    A semi-algebraic map is a function from a space to itself whose domain and graph are unions of solutions to systems of polynomial equations and inequalities. Thus it is a very general object with many applications, some from population genetics. The isoclines of such a map are semi-algebraic sets, which enjoy many striking properties, the most consequential of which here is that there is an algorithm to compute a "cylindrical decomposition" adapted to any finite family of semi-algebraic sets. The main subject of this paper is that a cylindrical decomposition adapted to the isoclines of a semi-algebraic map partitions parameter space into a tree which isolates bifurcations.
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    ItemOpen Access
    Sensitivity analysis of the basic reproduction number and other quantities for infectious disease models
    (Colorado State University. Libraries, 2012) Mikucki, Michael A., author; Tavener, Simon, advisor; Shipman, Patrick, committee member; Antolin, Michael, committee member
    Performing forward sensitivity analysis has been an integral component of mathematical modeling, yet its implementation becomes increasingly difficult with a model's complexity. For infectious disease models in particular, the sensitivity analysis of a parameter known as the basic reproduction number, or R0, has dominated the attention of ecology modelers. While the biological definition of R0 is well established, its mathematical construction is elusive. An index with a concrete mathematical definition that in many cases matches the biological interpretation of R0 is presented. A software package called Sensai that automatically computes this index and its sensitivity analysis is also presented. Other "quantities of interest" that provide similar information to R0 can also be implemented in Sensai and their sensitivities computed. Finally, some example models are presented and analyzed using Sensai.