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# Global Stability of Virus Spreading in Complex Heterogeneous Networks

Lin Wang and Guan-Zhong Dai
SIAM Journal on Applied Mathematics
Vol. 68, No. 5 (2008), pp. 1495-1502
Stable URL: http://www.jstor.org/stable/40233579
Page Count: 8
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## Abstract

Various networks are possessed of an obvious heterogeneity in the connectivity properties, and it is of practical significance to study epidemic spreading in networks of this kind. Pastor-Satorras and Vespignani established the dynamical mean-field reaction rate equations for the spreading of infections in complex heterogeneous networks based on the well-known SIS model, and figured out an epidemic threshold $\lambda _c$ such that if λ (effective spreading rate) is above $\lambda _c$ , the infection spreads and becomes endemic. The significance of this result is far-reaching; however, the authors have not found a strict mathematical proof of their conclusion in the literature. In this paper, we approach this problem by proving that if λ is above $\lambda _c$ , the infection spreads and approaches the unique positive stationary point of the reaction rate equations as long as there exist infected nodes in the network initially; i.e., the virus infection process is globally stable.

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