2026-09-20T13:28:17Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/907002026-09-02T13:52:16Zcom_10339_14934col_10339_38132

Fries, William 2018-05-24T08:36:00Z 2018-05-24T08:36:00Z 2018 https://wakespace.lib.wfu.edu/handle/10339/90700 In this paper we explore the introductory theory of modeling epidemics on networks and the significance of the spectral radius in their analysis. We look to establish properties of the spectral radius that would better inform how an epidemic might spread over such a network. We construct a specific transformation of networks that describe a transition from a star network to a path network. For the sequence of adjacency matrices that describe this transition, we show the spectral radius of these graphs can be given in a simple algebraic equation. Using this equation we show the spectral radius increases as the star unfolds and establish bounds on the spectral radius for each network. en Wake Forest University Epidemics Linear Algebra Spectral Graph Theory Characterizing the Spectral Radius of a Sequence of Adjacency Matrices Thesis Jiang, Miaohua Berenhaut, Kenneth Ballard, Grey Mathematics and Statistics open.access