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Epidemic spreading with time delay on complex networks

Epidemic spreading with time delay on complex networks In this paper, we propose a susceptible-infected-susceptible (SIS) model on complex networks, small-world (WS) networks and scale-free (SF) networks, to study the epidemic spreading behavior with time delay which is added into the infected phase. Considering the uniform delay, the basic reproduction number R 0 on WS networks and $$\bar R_0$$ on SF networks are obtained respectively. On WS networks, if R 0 ≤ 1, there is a disease-free equilibrium and it is locally asymptotically stable; if R 0 > 1, there is an epidemic equilibrium and it is locally asymptotically stable. On SF networks, if $$\bar R_0 \leqslant 1$$ , there is a disease-free equilibrium; if $$\bar R_0 > 1$$ , there is an epidemic equilibrium. Finally, we carry out simulations to verify the conclusions and analyze the effect of the time delay τ, the effective rate λ, average connectivity ⟨k⟩ and the minimum connectivity m on the epidemic spreading. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Epidemic spreading with time delay on complex networks

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-016-0554-1
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose a susceptible-infected-susceptible (SIS) model on complex networks, small-world (WS) networks and scale-free (SF) networks, to study the epidemic spreading behavior with time delay which is added into the infected phase. Considering the uniform delay, the basic reproduction number R 0 on WS networks and $$\bar R_0$$ on SF networks are obtained respectively. On WS networks, if R 0 ≤ 1, there is a disease-free equilibrium and it is locally asymptotically stable; if R 0 > 1, there is an epidemic equilibrium and it is locally asymptotically stable. On SF networks, if $$\bar R_0 \leqslant 1$$ , there is a disease-free equilibrium; if $$\bar R_0 > 1$$ , there is an epidemic equilibrium. Finally, we carry out simulations to verify the conclusions and analyze the effect of the time delay τ, the effective rate λ, average connectivity ⟨k⟩ and the minimum connectivity m on the epidemic spreading.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Apr 29, 2016

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