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Global analysis of multiple routes of disease transmission on heterogeneous networks

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  • Wang, Yi
  • Jin, Zhen

Abstract

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number R0 by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes.

Suggested Citation

  • Wang, Yi & Jin, Zhen, 2013. "Global analysis of multiple routes of disease transmission on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3869-3880.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:18:p:3869-3880
    DOI: 10.1016/j.physa.2013.03.042
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    References listed on IDEAS

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    1. Wang, Jia-zeng & Liu, Zeng-rong & Xu, Jianhua, 2007. "Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 715-721.
    2. Klovdahl, Alden S., 1985. "Social networks and the spread of infectious diseases: The AIDS example," Social Science & Medicine, Elsevier, vol. 21(11), pages 1203-1216, January.
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    Cited by:

    1. Zhou, Jiaying & Zhao, Yi & Ye, Yong, 2022. "Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    2. Wu, Yucui & Zhang, Zhipeng & Song, Limei & Xia, Chengyi, 2024. "Global stability analysis of two strains epidemic model with imperfect vaccination and immunity waning in a complex network," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Yang, Qian & Huo, Hai-Feng & Xiang, Hong, 2023. "Analysis of an edge-based SEIR epidemic model with sexual and non-sexual transmission routes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Zhu, Hongmiao & Jin, Zhen & Yan, Xin, 2022. "A dynamics model of two kinds of knowledge transmission on duplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    5. Yuan, Xinpeng & Wang, Fang & Xue, Yakui & Liu, Maoxing, 2018. "Global stability of an SIR model with differential infectivity on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 443-456.

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