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2015, 12(3): 609-623. doi: 10.3934/mbe.2015.12.609

Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks

1. 

Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506-5204, United States, United States

2. 

K-State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, 2061 Rathbone Hall, Manhattan, KS 66506-5204

3. 

Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, United States

4. 

Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104-6391, United States

Received  August 2014 Revised  December 2014 Published  February 2015

Launching a prevention campaign to contain the spread of infection requires substantial financial investments; therefore, a trade-off exists between suppressing the epidemic and containing costs. Information exchange among individuals can occur as physical contacts (e.g., word of mouth, gatherings), which provide inherent possibilities of disease transmission, and non-physical contacts (e.g., email, social networks), through which information can be transmitted but the infection cannot be transmitted. Contact network (CN) incorporates physical contacts, and the information dissemination network (IDN) represents non-physical contacts, thereby generating a multilayer network structure. Inherent differences between these two layers cause alerting through CN to be more effective but more expensive than IDN. The constraint for an epidemic to die out derived from a nonlinear Perron-Frobenius problem that was transformed into a semi-definite matrix inequality and served as a constraint for a convex optimization problem. This method guarantees a dying-out epidemic by choosing the best nodes for adopting preventive behaviors with minimum monetary resources. Various numerical simulations with network models and a real-world social network validate our method.
Citation: Heman Shakeri, Faryad Darabi Sahneh, Caterina Scoglio, Pietro Poggi-Corradini, Victor M. Preciado. Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks. Mathematical Biosciences & Engineering, 2015, 12 (3) : 609-623. doi: 10.3934/mbe.2015.12.609
References:
[1]

O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1994. doi: 10.1017/CBO9780511624100.

[2]

A. L. Barabasi and R. Albert, Emergence of Scaling in Random Networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.

[3]

S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, in Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001.

[4]

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. doi: 10.1017/CBO9780511804441.

[5]

D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec and C. Faloutsos, Epidemic Thresholds in Real Networks, ACM Trans. Inf. Syst. Secur., 10 (2008), 1-26. doi: 10.1145/1284680.1284681.

[6]

A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics, 9 (1962), 181-186. doi: 10.1002/nav.3800090303.

[7]

F. Darabi Sahneh, F. N. Chowdhury and C. Scoglio, On the Existence of a Threshold for Preventive Behavioral Responses to Suppress Epidemic Spreading, Sci. Rep., 2012. doi: 10.1038/srep00632.

[8]

F. Darabi Sahneh and C. Scoglio, Epidemic spread in human networks, in 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), (2011), 3008-3013.

[9]

F. Darabi Sahneh and C. Scoglio, Optimal information dissemination in epidemic networks, in 51st Annual Conference on Decision and Control (CDC), IEEE, (2012), 1657-1662. doi: 10.1109/CDC.2012.6425833.

[10]

M. Dickison, S. Havlin and H. E. Stanley, Epidemics on interconnected networks, Physical Review, 85 (2012), 066109. doi: 10.1103/PhysRevE.85.066109.

[11]

R. Diestel, Graph Theory, Springer Graduate Texts in Mathematics (GTM), 2012.

[12]

S. Funk and V. A. Jansen, Interacting epidemics on overlay networks epidemic spreading in multiplex networks, Physical Review, 81 (2010), 036118.

[13]

A. Ganesh, L. Massoulie and D. Towsley, The effect of network topology on the spread of epidemics, in INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE,2 (2005), 1455-1466. doi: 10.1109/INFCOM.2005.1498374.

[14]

C. Granell, S. Gómez and A. Arenas, Dynamical interplay between awareness and epidemic spreading in multiplex networks, Physical review letters, 111 (2013), 128701. doi: 10.1103/PhysRevLett.111.128701.

[15]

M. C. Grant, S. Boyd and Y. Ye, CVX: Matlab software for disciplined convex programming (web page and software), Available from: http://cvxr.com/cvx.

[16]

J. Kuczynski and H. Wozniakowski, Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start, SIAM journal on matrix analysis and applications, 13 (1992), 1094-1122. doi: 10.1137/0613066.

[17]

B. Lemmens and R. Nussbaum, Nonlinear Perron-Frobenius Theory, Cambridge University Press, 2012. doi: 10.1017/CBO9781139026079.

[18]

Y. Nesterov, Smoothing technique and its applications in semidefinite optimization, Science, 110 (2007), 245-259. doi: 10.1007/s10107-006-0001-8.

[19]

Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming, Society for Industrial and Applied Mathematics, 1994. doi: 10.1137/1.9781611970791.

[20]

M. Penrose, Random Geometric Graphs, Oxford University Press, 2003. doi: 10.1093/acprof:oso/9780198506263.001.0001.

[21]

V. M. Preciado, D. Sahneh and C. Scoglio, A convex framework for optimal investment on disease awareness in social networks, in Global Conference on Signal and Information Processing (GlobalSIP), IEEE, (2013), 851-854. doi: 10.1109/GlobalSIP.2013.6737025.

[22]

A. Saumell-Mendiola, M. A. Serrano and M. Bogu, Epidemic spreading on interconnected networks, Physical Review, 86 (2012), 026106. doi: 10.1103/PhysRevE.86.026106.

[23]

P. Schumm, W. Schumm and C. Scoglio, Impact of Preventive Responses to Epidemics in Rural Regions, PloS one, 8 (2013), e59028. doi: 10.1371/journal.pone.0059028.

[24]

G. Sun, Pattern formation of an epidemic model with diffusion, Nonlinear Dyn, 69 (2012), 1097-1104. doi: 10.1007/s11071-012-0330-5.

[25]

G. Sun, Q. Liu, Zh. Jin, A. Chakraborty and B. Li, Influence of infection rate and migration on extinction of disease in spatial epidemics, Journal of Theoretical Biology, 264 (2010), 95-103. doi: 10.1016/j.jtbi.2010.01.006.

[26]

P. Van Mieghem, The N-intertwined SIS epidemic network model, Computing, 93 (2011), 147-169. doi: 10.1007/s00607-011-0155-y.

[27]

P. Van Mieghem, J. Omic and R. Kooij, Epidemic Thresholds in Real Networks, IEEE/ACM Transactions on Networking, 17 (2009), 1-14.

[28]

O. Yaǧan and V. Gligor, Analysis of complex contagions in random multiplex networks, Physical Review, 86 (2012), 036103.

show all references

References:
[1]

O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1994. doi: 10.1017/CBO9780511624100.

[2]

A. L. Barabasi and R. Albert, Emergence of Scaling in Random Networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.

[3]

S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, in Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001.

[4]

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. doi: 10.1017/CBO9780511804441.

[5]

D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec and C. Faloutsos, Epidemic Thresholds in Real Networks, ACM Trans. Inf. Syst. Secur., 10 (2008), 1-26. doi: 10.1145/1284680.1284681.

[6]

A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics, 9 (1962), 181-186. doi: 10.1002/nav.3800090303.

[7]

F. Darabi Sahneh, F. N. Chowdhury and C. Scoglio, On the Existence of a Threshold for Preventive Behavioral Responses to Suppress Epidemic Spreading, Sci. Rep., 2012. doi: 10.1038/srep00632.

[8]

F. Darabi Sahneh and C. Scoglio, Epidemic spread in human networks, in 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), (2011), 3008-3013.

[9]

F. Darabi Sahneh and C. Scoglio, Optimal information dissemination in epidemic networks, in 51st Annual Conference on Decision and Control (CDC), IEEE, (2012), 1657-1662. doi: 10.1109/CDC.2012.6425833.

[10]

M. Dickison, S. Havlin and H. E. Stanley, Epidemics on interconnected networks, Physical Review, 85 (2012), 066109. doi: 10.1103/PhysRevE.85.066109.

[11]

R. Diestel, Graph Theory, Springer Graduate Texts in Mathematics (GTM), 2012.

[12]

S. Funk and V. A. Jansen, Interacting epidemics on overlay networks epidemic spreading in multiplex networks, Physical Review, 81 (2010), 036118.

[13]

A. Ganesh, L. Massoulie and D. Towsley, The effect of network topology on the spread of epidemics, in INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE,2 (2005), 1455-1466. doi: 10.1109/INFCOM.2005.1498374.

[14]

C. Granell, S. Gómez and A. Arenas, Dynamical interplay between awareness and epidemic spreading in multiplex networks, Physical review letters, 111 (2013), 128701. doi: 10.1103/PhysRevLett.111.128701.

[15]

M. C. Grant, S. Boyd and Y. Ye, CVX: Matlab software for disciplined convex programming (web page and software), Available from: http://cvxr.com/cvx.

[16]

J. Kuczynski and H. Wozniakowski, Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start, SIAM journal on matrix analysis and applications, 13 (1992), 1094-1122. doi: 10.1137/0613066.

[17]

B. Lemmens and R. Nussbaum, Nonlinear Perron-Frobenius Theory, Cambridge University Press, 2012. doi: 10.1017/CBO9781139026079.

[18]

Y. Nesterov, Smoothing technique and its applications in semidefinite optimization, Science, 110 (2007), 245-259. doi: 10.1007/s10107-006-0001-8.

[19]

Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming, Society for Industrial and Applied Mathematics, 1994. doi: 10.1137/1.9781611970791.

[20]

M. Penrose, Random Geometric Graphs, Oxford University Press, 2003. doi: 10.1093/acprof:oso/9780198506263.001.0001.

[21]

V. M. Preciado, D. Sahneh and C. Scoglio, A convex framework for optimal investment on disease awareness in social networks, in Global Conference on Signal and Information Processing (GlobalSIP), IEEE, (2013), 851-854. doi: 10.1109/GlobalSIP.2013.6737025.

[22]

A. Saumell-Mendiola, M. A. Serrano and M. Bogu, Epidemic spreading on interconnected networks, Physical Review, 86 (2012), 026106. doi: 10.1103/PhysRevE.86.026106.

[23]

P. Schumm, W. Schumm and C. Scoglio, Impact of Preventive Responses to Epidemics in Rural Regions, PloS one, 8 (2013), e59028. doi: 10.1371/journal.pone.0059028.

[24]

G. Sun, Pattern formation of an epidemic model with diffusion, Nonlinear Dyn, 69 (2012), 1097-1104. doi: 10.1007/s11071-012-0330-5.

[25]

G. Sun, Q. Liu, Zh. Jin, A. Chakraborty and B. Li, Influence of infection rate and migration on extinction of disease in spatial epidemics, Journal of Theoretical Biology, 264 (2010), 95-103. doi: 10.1016/j.jtbi.2010.01.006.

[26]

P. Van Mieghem, The N-intertwined SIS epidemic network model, Computing, 93 (2011), 147-169. doi: 10.1007/s00607-011-0155-y.

[27]

P. Van Mieghem, J. Omic and R. Kooij, Epidemic Thresholds in Real Networks, IEEE/ACM Transactions on Networking, 17 (2009), 1-14.

[28]

O. Yaǧan and V. Gligor, Analysis of complex contagions in random multiplex networks, Physical Review, 86 (2012), 036103.

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