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Abstract

Imagine you are walking down a crowded hallway. You aren't in contact with everyone all at once. You talk to or simply pass by different people at different times as you walk down the hall. These connections would best be represented using a temporal network. In this work, we examine temporal networks to determine the behavior of disease spread across these networks and how it differs from the behavior of static networks. We use differential equations for mean field approximations to theoretically model how infection spreads throughout a temporal network. We extend our model to incorporate network structure by deriving a degree-based mean field theory. We then validate our theories with simulations in Mathematica. We also look into including multiple rounds of infections to see how it affects the spreading behavior. From our results we are able to determine how the temporal aspect affects the rate of spread of the disease and the overall size of the infected population.

Author Bio

Catherine Northrup is currently an undergraduate at Carthage College in Kenosha, Wisconsin aiming for a degree in Mathematics with a minor in Physics. She intends to attend graduate school after completing at Carthage. On the side, she enjoys writing fiction and classic pencil drawing.

Elisabeth Rutter is currently an undergraduate student at Carthage College in Kenosha, Wisconsin studying mathematics and chemistry. She is working toward receiving a Bachelor’s Degree in both areas of study and hopes to attend graduate school in the future.

Kerry Stapf is currently an undergraduate at Carthage College in Kenosha, Wisconsin, working towards a Bachelor’s Degree with a major in mathematics and a minor in chemistry. She enjoys reading, baking, and knitting in her spare time.

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