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Dynamic analysis of a delayed model for vector-borne diseases on bipartite networks

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  • Zhang, Ruixia
  • Li, Deyu
  • Jin, Zhen

Abstract

In this paper, to study the spread of vector-borne diseases in human population, we build two coupled models for human population and vector population respectively on bipartite networks. By taking approximate expression for the density of infective vectors, we reduce the coupled models to a delayed SIS model describing the spread of diseases in human population. For the delayed dynamic model, we analyze its dynamic behavior. The basic reproduction number R0 is given. And based on the Lyapunov–LaSalle invariance principle, we prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium. Finally we carry out simulations to verify the conclusions and reveal the effect of the topology structure of networks and the time delay on the transmission process. Our results show that the basic reproduction number depends on the topology structure of bipartite networks and the time delay. It is also pointed out that the time delay can reduce the basic reproduction number. Furthermore, when the disease will disappear, the delay speeds up the disappearing process; when disease will become endemic, the delay slows the disease spreading down and reduces the density of infective humans.

Suggested Citation

  • Zhang, Ruixia & Li, Deyu & Jin, Zhen, 2015. "Dynamic analysis of a delayed model for vector-borne diseases on bipartite networks," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 342-352.
  • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:342-352
    DOI: 10.1016/j.amc.2015.04.074
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    References listed on IDEAS

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    1. Yang, Meng & Chen, Guanrong & Fu, Xinchu, 2011. "A modified SIS model with an infective medium on complex networks and its global stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2408-2413.
    2. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    3. Shi, Hongjing & Duan, Zhisheng & Chen, Guanrong, 2008. "An SIS model with infective medium on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2133-2144.
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    Cited by:

    1. Chuangxia Huang & Jie Cao & Fenghua Wen & Xiaoguang Yang, 2016. "Stability Analysis of SIR Model with Distributed Delay on Complex Networks," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-22, August.
    2. Zhang, Ruixia, 2020. "Global dynamic analysis of a model for vector-borne diseases on bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.

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