#### Event Title

Chronology of Epidemics in Aggregated Temporal Networks

#### Location

Science Center A254

#### Start Date

10-28-2016 2:00 PM

#### End Date

10-28-2016 3:20 PM

#### Research Program

Research Experiences for Undergraduates (REU) program, Santa Fe Institute

#### Abstract

Epidemic propagation on temporal, or time-varying, social contact networks is a developing area in network science. Given the adjacency matrices for two timesteps of the same underlying network, A and B, it is difficult to tell to what extent an epidemic spreading process will obey the chronology of the network if the two timesteps are aggregated into one fixed network, A+B. The solution to a system of differential equations modeling a diffusion process on the adjacency matrix for a particular network can be found using the matrix exponential. We use this method as an analogy for the epidemic spreading process on a social contact network. The product of the matrix exponential for two non-commuting matrices A and B yields an expression in terms of the aggregate A+B with a specified error term involving the commutator of the two matrices, AB-BA. We derive analytical measures to quantify the significance of the error term in the matrix exponential, and explore their relationship with measures of error from simulated epidemic propagation on temporal versus aggregated versions of the network.

#### Recommended Citation

Allen, Andrea, "Chronology of Epidemics in Aggregated Temporal Networks" (2016). *Celebration of Undergraduate Research*. 1.

https://digitalcommons.oberlin.edu/cour/2016/panel_03/1

#### Major

Mathematics

#### Project Mentor(s)

Laurent Hébert-Dufresne, The Santa Fe Institute

#### Document Type

Presentation

Chronology of Epidemics in Aggregated Temporal Networks

Science Center A254

Epidemic propagation on temporal, or time-varying, social contact networks is a developing area in network science. Given the adjacency matrices for two timesteps of the same underlying network, A and B, it is difficult to tell to what extent an epidemic spreading process will obey the chronology of the network if the two timesteps are aggregated into one fixed network, A+B. The solution to a system of differential equations modeling a diffusion process on the adjacency matrix for a particular network can be found using the matrix exponential. We use this method as an analogy for the epidemic spreading process on a social contact network. The product of the matrix exponential for two non-commuting matrices A and B yields an expression in terms of the aggregate A+B with a specified error term involving the commutator of the two matrices, AB-BA. We derive analytical measures to quantify the significance of the error term in the matrix exponential, and explore their relationship with measures of error from simulated epidemic propagation on temporal versus aggregated versions of the network.

## Notes

Session I, Panel 3 - Networks & Models