Open Access
2012 Modeling and Analysis of Epidemic Diffusion within Small-World Network
Ming Liu, Yihong Xiao
J. Appl. Math. 2012(SI10): 1-14 (2012). DOI: 10.1155/2012/841531


To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS) model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS) model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.


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Ming Liu. Yihong Xiao. "Modeling and Analysis of Epidemic Diffusion within Small-World Network." J. Appl. Math. 2012 (SI10) 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.91051
MathSciNet: MR2948084
Digital Object Identifier: 10.1155/2012/841531

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI10 • 2012
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