In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by...In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^＊, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition.展开更多
A method is proposed to find key components of traffic networks with homogenous and heterogeneous topologies, in which heavier traffic flow is transported. One component, called the skeleton, is the minimum spanning t...A method is proposed to find key components of traffic networks with homogenous and heterogeneous topologies, in which heavier traffic flow is transported. One component, called the skeleton, is the minimum spanning tree (MST) based on the zero flow cost (ZCMST). The other component is the infinite incipient percolation cluster (IIC) which represents the spine of the traffic network. Then, a new method to analysis the property of the bottleneck in a large scale traffic network is given from a macroscopic and statistical viewpoint. Moreover, three effective strategies are proposed to alleviate traffic congestion. The significance of the findings is that one can significantly improve the global transport by enhancing the capacity in the ZCMST with a few links, while for improving the local traffic property, improving a tiny fraction of the traffic network in the IIC is effective. The result can be used to help traffic managers prevent and alleviate traffic congestion in time, guard against the formation of congestion bottleneck, and make appropriate policies for traffic demand management. Meanwhile, the method has very important theoretical significance and practical worthiness in optimizing traffic organization, traffic control, and disposal of emergency.展开更多
基金Project supported by the Science Foundation of Shanxi Province of China (Grant No 2009011005-1)the Youth Foundation of Shanxi Province of China (Grant No 2007021006)
文摘In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^＊, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition.
基金Supported by the National Basic Research Program of China ("973" Project) (Grant No. 2006CB705500)the FANEDD (Grant No. 200763)+1 种基金the National Natural Science Foundation of China (Grant Nos. 70801005, 70871099)the Foundation of State Key Laboratory of Rail Control and Safety (Grant No. RCS2008ZZ001)
文摘A method is proposed to find key components of traffic networks with homogenous and heterogeneous topologies, in which heavier traffic flow is transported. One component, called the skeleton, is the minimum spanning tree (MST) based on the zero flow cost (ZCMST). The other component is the infinite incipient percolation cluster (IIC) which represents the spine of the traffic network. Then, a new method to analysis the property of the bottleneck in a large scale traffic network is given from a macroscopic and statistical viewpoint. Moreover, three effective strategies are proposed to alleviate traffic congestion. The significance of the findings is that one can significantly improve the global transport by enhancing the capacity in the ZCMST with a few links, while for improving the local traffic property, improving a tiny fraction of the traffic network in the IIC is effective. The result can be used to help traffic managers prevent and alleviate traffic congestion in time, guard against the formation of congestion bottleneck, and make appropriate policies for traffic demand management. Meanwhile, the method has very important theoretical significance and practical worthiness in optimizing traffic organization, traffic control, and disposal of emergency.
