American Institute of Mathematical Sciences

Advanced
2005, 2(2): 317-327. doi: 10.3934/mbe.2005.2.317

Thresholds for Epidemic Outbreaks in Finite Scale-Free Networks

Dong-Uk Hwang 1, , S. Boccaletti 2, , Y. Moreno 3, and  R. López-Ruiz 4,

1. 

Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6 50125 Florence, Italy
2. 

Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6, 50125 Florence
3. 

Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza 50009, Spain
4. 

Department of Computer Science, University of Zaragoza, Zaragoza 50009, Spain

Received  October 2004 Revised  February 2005 Published  March 2005

We numerically investigate the existence of a threshold for epidemic outbreaks in a class of scale-free networks characterized by a parametrical dependence of the scaling exponent, influencing the convergence of fluctuations in the degree distribution. In finite-size networks, finite thresholds for the spreading of an epidemic are always found. However, both the thresholds and the behavior of the epidemic prevalence are quite different with respect to the type of network considered and the system size. We also discuss agreements and differences with some analytical claims previously reported.
Keywords: scale-free network., epidemic threshold.
Mathematics Subject Classification: 92D3.
Citation: Dong-Uk Hwang, S. Boccaletti, Y. Moreno, R. López-Ruiz. Thresholds for Epidemic Outbreaks in Finite Scale-Free Networks. Mathematical Biosciences & Engineering, 2005, 2 (2) : 317-327. doi: 10.3934/mbe.2005.2.317
[1]

Matthias Täufer, Martin Tautenhahn. Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1719-1730. doi: 10.3934/cpaa.2017083
[2]

Roberto Serra, Marco Villani, Alex Graudenzi, Annamaria Colacci, Stuart A. Kauffman. The simulation of gene knock-out in scale-free random Boolean models of genetic networks. Networks & Heterogeneous Media, 2008, 3 (2) : 333-343. doi: 10.3934/nhm.2008.3.333
[3]

Junling Ma, Zhien Ma. Epidemic threshold conditions for seasonally forced SEIR models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 161-172. doi: 10.3934/mbe.2006.3.161
[4]

Mehrdad Nojoumian, Douglas R. Stinson. On dealer-free dynamic threshold schemes. Advances in Mathematics of Communications, 2013, 7 (1) : 39-56. doi: 10.3934/amc.2013.7.39
[5]

Bailey Kacsmar, Douglas R. Stinson. A network reliability approach to the analysis of combinatorial repairable threshold schemes. Advances in Mathematics of Communications, 2019, 13 (4) : 601-612. doi: 10.3934/amc.2019037
[6]

Lin Zhao, Zhi-Cheng Wang, Liang Zhang. Threshold dynamics of a time periodic and two–group epidemic model with distributed delay. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1535-1563. doi: 10.3934/mbe.2017080
[7]

Toshikazu Kuniya, Yoshiaki Muroya, Yoichi Enatsu. Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1375-1393. doi: 10.3934/mbe.2014.11.1375
[8]

Yanan Zhao, Daqing Jiang, Xuerong Mao, Alison Gray. The threshold of a stochastic SIRS epidemic model in a population with varying size. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1277-1295. doi: 10.3934/dcdsb.2015.20.1277
[9]

Liang Zhang, Zhi-Cheng Wang. Threshold dynamics of a reaction-diffusion epidemic model with stage structure. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3797-3820. doi: 10.3934/dcdsb.2017191
[10]

Yijun Lou, Xiao-Qiang Zhao. Threshold dynamics in a time-delayed periodic SIS epidemic model. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 169-186. doi: 10.3934/dcdsb.2009.12.169
[11]

Adel Settati, Aadil Lahrouz, Mustapha El Jarroudi, Mohamed El Fatini, Kai Wang. On the threshold dynamics of the stochastic SIRS epidemic model using adequate stopping times. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1985-1997. doi: 10.3934/dcdsb.2020012
[12]

Tomás Caraballo, Mohamed El Fatini, Idriss Sekkak, Regragui Taki, Aziz Laaribi. A stochastic threshold for an epidemic model with isolation and a non linear incidence. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2513-2531. doi: 10.3934/cpaa.2020110
[13]

Shuping Li, Zhen Jin. Impacts of cluster on network topology structure and epidemic spreading. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3749-3770. doi: 10.3934/dcdsb.2017187
[14]

Jia-Feng Cao, Wan-Tong Li, Fei-Ying Yang. Dynamics of a nonlocal SIS epidemic model with free boundary. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 247-266. doi: 10.3934/dcdsb.2017013
[15]

Arti Mishra, Benjamin Ambrosio, Sunita Gakkhar, M. A. Aziz-Alaoui. A network model for control of dengue epidemic using sterile insect technique. Mathematical Biosciences & Engineering, 2018, 15 (2) : 441-460. doi: 10.3934/mbe.2018020
[16]

Cheng-Ta Yeh, Yi-Kuei Lin. Component allocation cost minimization for a multistate computer network subject to a reliability threshold using tabu search. Journal of Industrial & Management Optimization, 2016, 12 (1) : 141-167. doi: 10.3934/jimo.2016.12.141
[17]

Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565
[18]

Lili Liu, Xianning Liu, Jinliang Wang. Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2615-2630. doi: 10.3934/dcdsb.2016064
[19]

Haomin Huang, Mingxin Wang. The reaction-diffusion system for an SIR epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2039-2050. doi: 10.3934/dcdsb.2015.20.2039
[20]

Meng Zhao, Wan-Tong Li, Wenjie Ni. Spreading speed of a degenerate and cooperative epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 981-999. doi: 10.3934/dcdsb.2019199

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences