Stability analysis of generalized epidemic models over directed networks

Proceedings of the IEEE Conference on Decision and Control

Volumn 2015-February, Issue February, 2014, Pages 6197-6202

  Nowzari, Cameron ^a   Preciado, Victor M ^a   Pappas, George J ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIRECTED GRAPHS; LINEAR SYSTEMS; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS;

ARBITRARY DIRECTED GRAPHS; CO-ORDINATE TRANSFORMATION; DISEASE SPREADING; DISEASE-FREE EQUILIBRIUM; GLOBALLY EXPONENTIALLY STABLE; HEALTHY INDIVIDUALS; NONLINEAR STABILITY ANALYSIS; STABILITY ANALYSIS;

EPIDEMIOLOGY;

EID: 84959489007     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2014.7040360     Document Type: Conference Paper

References (21)

1. N. T. Bailey, The Mathematical Theory of Infectious Diseases and its Applications. London: Griffin, 1975.
2. Y. Hu, H. Chen, J. Lou, and J. Li, "Epidemic spreading in real networks: An eigenvalue viewpoint," in Proc. Symp. Reliable Distributed Systems, pp. 25-34, 2003.
3. P. V. Miegham, J. Omic, and R. Kooij, "Virus spread in networks," IEEE/ACM Transactions on Networking, Vol. 17, no. 1, pp. 1-14, 2009.
4. H. J. Ahn and B. Hassibi, "Global dynamics of epidemic spread over complex networks," in IEEE Conf. on Decision and Control, (Florence, Italy), pp. 4579-4585, 2013.
5. M. M. Williamson and J. Leveille, "An epidemiological model of virus spread and cleanup," in Virus Bulletin, (Toronto, Canada), 2003.
6. M. Garetto, W. Gong, and D. Towsley, "Modeling malware spreading dynamics," in INFOCOM Joint Conference of the IEEE Computer and Communications, pp. 1869-1879, 2003.
7. D. Easley and J. Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.
8. P. V. Mieghem and J. Omic, "In-homogeneous virus spread in networks," 2014. http://arxiv.org/pdf/1306.2588.pdf.
9. S. Funk, E. Gilad, C. Watkins, and V. A. A. Jansen, "The spread of awareness and its impact on epidemic outbreaks," Proceedings of the National Academy of Sciences, Vol. 16, no. 106, 2009.
10. N. Furguson, "Capturing human behaviour," Nature, Vol. 733, no. 446, 2007.
11. S. Funk, M. Salathe, and V. A. A. Jansen, "Modelling the influence of human behaviour on the spread of infectious diseases: a review," Journal of The Royal Society Interface, Vol. 7, no. 50, pp. 1247-1256, 2010.
12. F. D. Sabneh and C. Scoglio, "Epidemic spread in human networks," in IEEE Conf. on Decision and Control, (Orlando, FL), pp. 3008-3013, 2011.
13. B. A. Prakash, D. Chakrabarti, M. Faloutsos, N. Valler, and C. Faloutsos, "Got the flu (or mumps)? check the eigenvalue!," 2010. http://arxiv.org/abs/1004.0060.
14. H. W. Hethcote, "The mathematics of infectious diseases," SIAM Review, Vol. 42, no. 4, pp. 599-653, 2000.
15. J. Li, Y. Yang, and Y. Zhou, "Global stability of an epidemic model with latent stage and vaccination," Nonlinear Analysis: Real World Applications, Vol. 12, no. 4, pp. 2163-2173, 2011.
16. M. M. Hikal, "Dynamic properties for a general SEIV epidemic model," SIAM Review, Vol. 2, no. 1, pp. 26-36, 2014.
17. Y. Wan, S. Roy, and A. Saberi, "Designing spatially heterogeneous strategies for control of virus spread," IET Systems Biology, Vol. 2, no. 4, pp. 184-201, 2008.
18. V. M. Preciado, M. Zargham, C. Enyioha, A. Jadbabaie, and G. J. Pappas, "Optimal resource allocation for network protection: A geometric programming approach," IEEE Transactions on Networked Control Systems, 2013. accepted.
19. V. M. Preciado, M. Zargham, C. Enyioha, A. Jadbabaie, and G. J. Pappas, "Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks," in IEEE Conf. on Decision and Control, (Florence, Italy), pp. 7486-7491, 2013.
20. P. V. Mieghem, Performance Analysis of Communications Networks and Systems. Cambridge, UK: Cambridge University Press, 2009.
21. H. K. Khalil, Nonlinear Systems. Prentice Hall, 3 ed., 2002.