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Analysis of SE τ IR ω S epidemic disease models with vertical transmission in complex networks

Analysis of SE τ IR ω S epidemic disease models with vertical transmission in complex networks When the role of network topology is taken into consideration, one of the objectives is to understand the possible implications of topological structure on epidemic models. As most real networks can be viewed as complex networks, we propose a new delayed SE τ IR ω S epidemic disease model with vertical transmission in complex networks. By using a delayed ODE system, in a small-world (SW) network we prove that, under the condition R 0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R 0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R 0 > 1. In a scale-free (SF) network we obtain the condition R 1 > 1 under which the system will be of non-zero stationary prevalence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Analysis of SE τ IR ω S epidemic disease models with vertical transmission in complex networks

Acta Mathematicae Applicatae Sinica , Volume 28 (1) – Dec 14, 2011

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0094-1
Publisher site
See Article on Publisher Site

Abstract

When the role of network topology is taken into consideration, one of the objectives is to understand the possible implications of topological structure on epidemic models. As most real networks can be viewed as complex networks, we propose a new delayed SE τ IR ω S epidemic disease model with vertical transmission in complex networks. By using a delayed ODE system, in a small-world (SW) network we prove that, under the condition R 0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R 0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R 0 > 1. In a scale-free (SF) network we obtain the condition R 1 > 1 under which the system will be of non-zero stationary prevalence.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Dec 14, 2011

References