Publications by authors named "Zhongpu Xu"

3 Publications

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Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks.

Chaos 2019 Mar;29(3):033122

Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.

This paper investigates feedback pinning control of synchronization behaviors aroused by epidemic spread on complex networks. Based on the quenched mean field theory, epidemic control synchronization models with the inhibition of contact behavior are constructed, combined with the epidemic transmission system and the adaptive dynamical network carrying active controllers. By the properties of convex functions and the Gerschgorin theorem, the epidemic threshold of the model is obtained, and the global stability of disease-free equilibrium is analyzed. For individual's infected situation, when an epidemic disease spreads, two types of feedback control strategies depending on the diseases' information are designed: the first one only adds controllers to infected individuals, and the other adds controllers to both infected and susceptible ones. By using the Lyapunov stability theory, under designed controllers, some criteria that guarantee the epidemic controlled synchronization system achieving behavior synchronization are also derived. Several numerical simulations are performed to show the effectiveness of our theoretical results. As far as we know, this is the first work to address the controlled behavioral synchronization induced by epidemic spread under the pinning feedback mechanism. It is hopeful that we may have deeper insights into the essence between the disease's spread and collective behavior under active control in complex dynamical networks.
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http://dx.doi.org/10.1063/1.5047653DOI Listing
March 2019

Epidemic Spread on One-Way Circular-Coupled Networks.

Acta Math Sci 2019 27;39(6):1713-1732. Epub 2019 Sep 27.

Department of Mathematics, Shanghai University, Shanghai, 200444 China.

Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well.
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http://dx.doi.org/10.1007/s10473-019-0618-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7111949PMC
September 2019

Interaction between epidemic spread and collective behavior in scale-free networks with community structure.

J Theor Biol 2019 02 10;462:122-133. Epub 2018 Nov 10.

Department of Mathematics, Shanghai University, Shanghai 200444, China. Electronic address:

Many real-world networks exhibit community structure: the connections within each community are dense, while connections between communities are sparser. Moreover, there is a common but non-negligible phenomenon, collective behaviors, during the outbreak of epidemics, are induced by the emergence of epidemics and in turn influence the process of epidemic spread. In this paper, we explore the interaction between epidemic spread and collective behavior in scale-free networks with community structure, by constructing a mathematical model that embeds community structure, behavioral evolution and epidemic transmission. In view of the differences among individuals' responses in different communities to epidemics, we use nonidentical functions to describe the inherent dynamics of individuals. In practice, with the progress of epidemics, individual behaviors in different communities may tend to cluster synchronization, which is indicated by the analysis of our model. By using comparison principle and GersĖ˜gorin theorem, we investigate the epidemic threshold of the model. By constructing an appropriate Lyapunov function, we present the stability analysis of behavioral evolution and epidemic dynamics. Some numerical simulations are performed to illustrate and complement our theoretical results. It is expected that our work can deepen the understanding of interaction between cluster synchronization and epidemic dynamics in scale-free community networks.
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http://dx.doi.org/10.1016/j.jtbi.2018.11.003DOI Listing
February 2019