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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :63-74    DOI: 10.1007/s10255-012-0094-1
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Analysis of SEτIRωS Epidemic Disease Models with Vertical Transmission in Complex Networks
Xia LIU, De-ju XU
Department of Mathematics, Capital Normal University, Beijing 100048, China
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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 SEτIRωS 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 R0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R0 > 1. In a scale-free (SF) network we obtain the condition R1 > 1 under which the system will be of non-zero stationary prevalence.  
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KeywordsSEτIRωS   SW network   SF network   DFE     
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 SEτIRωS 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 R0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R0 > 1. In a scale-free (SF) network we obtain the condition R1 > 1 under which the system will be of non-zero stationary prevalence.  
KeywordsSEτIRωS,   SW network,   SF network,   DFE     
Received: 2011-04-20;
Cite this article:   
.Analysis of SEτIRωS Epidemic Disease Models with Vertical Transmission in Complex Networks[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 63-74
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0094-1      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/63
 
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