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Edge-based epidemic dynamics with multiple routes of transmission on random networks

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Abstract

This paper concerns the SIR dynamics with two types of spreading mechanism, i.e., local spreading through network contacts and global spreading through casual contacts. A low-dimensional edge-based model of ordinary differential equations incorporating arbitrary heterogeneous number of individual contacts is formulated. The basic reproduction number \(R_{0}\) is obtained, and on networks of Poisson type, it is the sum of the basic reproduction numbers for global and local spreading pathways; however, on networks of other type, it is a nonlinear function of the basic reproduction numbers for global and local spreading pathways. To measure the control efforts imposed on one specific transmission pathway, type reproduction numbers for global and local transmission pathways are calculated, respectively. Equations of the final epidemic size are analytically derived. Finally, the numerical solutions to our model are compared with the ensemble averages of the stochastic simulations. Simulations have shown that casual contacts in the population may trigger large stochastic fluctuations, which may cause huge variances around their mean; thus, in this scenario the ensemble mean is not a good representation of the behavior of the stochastic epidemic process. However, increasing the local infection rate or the connectedness of networks yields better predictions. The results presented provide insights in setting a framework for the analysis and containment of multiple routes of epidemic transmission in reality.

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Acknowledgements

The Project was supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG170622), and was partially supported by the National Natural Science Foundation of China under Grant Nos. 61573096 and 61272530.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Yi Wang

  2. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210996, China

    Jinde Cao

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jinde Cao

  4. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, China

    Xiaodi Li

  5. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

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  1. Yi Wang
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  2. Jinde Cao
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  4. Ahmed Alsaedi
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Correspondence to Yi Wang.

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Wang, Y., Cao, J., Li, X. et al. Edge-based epidemic dynamics with multiple routes of transmission on random networks. Nonlinear Dyn 91, 403–420 (2018). https://doi.org/10.1007/s11071-017-3877-3

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  • DOI: https://doi.org/10.1007/s11071-017-3877-3

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