p-Modulus on Networks with Applications to the Study of Epidemics

(Link to the official project webpage )

This project develops new mathematical theories and computational algorithms to capture the essential features of networks and applies them to models in epidemiology. Results from this project will allow researchers to identify a number of valuable patterns in the data, including the subpopulations at highest risk, vulnerable transmission pathways, and effective mitigation strategies. The investigators study the mathematical concept of p-modulus on networks, focusing on the analysis of theoretical properties, the development of numerical algorithms, and the study of applications to the spread of diseases in contact networks. This is an interdisciplinary project intended to enhance both the theoretical understanding of the ways in which diseases spread in an interconnected network of individuals or sub-populations, and the computational tools available to researchers interested in modeling, simulating, and predicting the behavior of epidemics.

Project duration September 15, 2015 - August 31, 2018

Investigators

Faculty

Nathan Albin (PI)
Pietro Poggi-Corradini (co-PI)
Caterina Scoglio (Google Profile) (co-PI)

Students

Aram Vajdi (Summer 2017-Present)
Heman Shakeri (Fall 2015-Spring 2017)

Products from The NetSE group

2017	Network-Centric Interventions to Contain the Syphilis Epidemic in San Francisco D Juher, J Saldaña, R Kohn, K Bernstein, C Scoglio Scientific Reports 7
2016	Maximizing algebraic connectivity in interconnected networks. H. Shakeri, N. Albin, F. Sahneh, P. Poggi-Corradini, and C. Scoglio. Physical Review E, Mar 93 (2016), 030301. [arxiv]
	Minimal subfamilies and the probabilistic interpretation for modulus on graphs. N. Albin and P. Poggi-Corradini. Journal of Analysis, (2016), 1-26. [arxiv]
	Modulus of families of walks on graphs. Nathan Albin, Pietro Poggi-Corradini, Faryad Darabi Sahneh, and Max Goering. Proceedings of Complex Analysis and Dynamical Systems VII,(2016), to appear. [arxiv]
	Generalized network measures based on modulus of families of walks. H. Shakeri, P. Poggi-Corradini, C. Scoglio, and N. Albin. Journal of Computational and Applied Mathematics, 307 (2016), 307-318.
2015	Numerical Investigation of Metrics for Epidemic Processes on Graphs. M. Goering, N. Albin, F. Sahneh, C. Scoglio, and P. Poggi-Corradini. 2015 49th Asilomar Conference on Signals, Systems and Computers,Nov (2015), 1317--1322. [arxiv]
	Modulus on graphs as a generalization of standard graph theoretic quantities. Nathan Albin, Megan Brunner, Roberto Perez, Pietro Poggi-Corradini, and Natalie Wiens. Conformal Geometry and Dynamics, 19 (2015), 298-317. [arxiv]
	Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks. Heman Shakeri, Faryad Darabi Sahneh, Caterina Scoglio, Pietro Poggi-Corradini, and Victor M. Preciado. Math. Biosci. Eng. 12(3), 12 (2015), 609--623.

Outreach

NODE group opportunities

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Supported by National Science Foundation under Award DMS -1515810.