Date of Submission

Spring 2018

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Lauren Rose

Abstract/Artist's Statement

In this project we model the spread of a virus on networks as a probabilistic process. We assume the virus breaks out at one vertex on a network and then spreads to neighboring vertices in each time step with a certain probability. Our objective is to find probability distributions that describe the uncertain number of infected vertices at a given time step. The networks we consider are paths, cycles, star graphs, complete graphs, and broom graphs. Through the use of Markov chains and Jordan Normal Form we analyze the probability distribution of these graphs, characterizing the transition matrix for each graph as well as the Jordan Form matrices.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Included in

Probability Commons

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