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.
Haley A. Yaple
Northrup, Catherine; Rutter, Elisabeth; and Stapf, Kerry
"SI Dynamics of Disease Spread,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17:
1, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol17/iss1/12