Epidemic spreading and global stability of an SIS model with an infective vector on complex networks

被引:92
作者
Kang, Huiyan [1 ,2 ]
Fu, Xinchu [1 ]
机构
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Changzhou Univ, Sch Math & Phys, Changzhou 213016, Jiangsu, Peoples R China
关键词
SIS model; Complex network; Epidemic threshold; Global stability; HETEROGENEOUS NETWORKS; MATHEMATICAL-THEORY; TRANSMISSION;
D O I
10.1016/j.cnsns.2015.02.018
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:30 / 39
页数:10
相关论文
共 28 条
[1]
Immunization of susceptible-infected model on scale-free networks [J].
Bai, Wen-He ;
Zhou, Tao ;
Wang, Bing-Hong .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 384 (02) :656-662
[2]
Bailey N., 1975, The mathematical theory of infectious diseases
[3]
Emergence of scaling in random networks [J].
Barabási, AL ;
Albert, R .
SCIENCE, 1999, 286 (5439) :509-512
[4]
Velocity and hierarchical spread of epidemic outbreaks in scale-free networks -: art. no. 178701 [J].
Barthélemy, M ;
Barrat, A ;
Pastor-Satorras, R ;
Vespignani, A .
PHYSICAL REVIEW LETTERS, 2004, 92 (17) :178701-1
[5]
Cooke K.L., 1979, The Rocky Mountain Journal of Mathematics, V9, P31, DOI DOI 10.1216/RMJ-1979-9-1-31
[6]
Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization [J].
Fu, Xinchu ;
Small, Michael ;
Walker, David M. ;
Zhang, Haifeng .
PHYSICAL REVIEW E, 2008, 77 (03)
[7]
Contributions to the mathematical theory of epidemics II - The problem of endemicity [J].
Kermack, WO ;
McKendrick, AG .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1932, 138 (834) :55-83
[8]
Contribution to the mathematical theory of epidemics [J].
Kermack, WO ;
McKendrick, AG .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721
[9]
MARTIN RH, 1991, J REINE ANGEW MATH, V413, P1
[10]
Epidemic outbreaks in complex heterogeneous networks [J].
Moreno, Y ;
Pastor-Satorras, R ;
Vespignani, A .
EUROPEAN PHYSICAL JOURNAL B, 2002, 26 (04) :521-529