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Estimating the state probability distribution for epidemic spreading in complex networks

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  • Schaum, Alexander
  • Bernal Jaquez, Roberto

Abstract

The problem of state estimation of spreading phenomena in complex networks is considered on the basis of a detectability-based approach. Using a simple, reduced model based state distribution estimator, where the monitored nodes are driven directly by the measured data, asymptotic convergence conditions are provided in terms of the number and location of the required sensors on the basis of the network topology. The convergence of the estimator is established in terms of the largest eigenvalue of a reduced connectivity matrix which stems from removing the monitored nodes and their connections from the original graph. In the case of unit weights, this condition corresponds to measuring the nodes with highest degree. Numerical simulations for a complete and a scale-free network each of 500 nodes and randomly distributed and unit weights, respectively, illustrate the estimator functioning with 20 sensors for the complete, and 38 sensors for the scale-free network.

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  • Schaum, Alexander & Bernal Jaquez, Roberto, 2016. "Estimating the state probability distribution for epidemic spreading in complex networks," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 197-206.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:197-206
    DOI: 10.1016/j.amc.2016.06.037
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    References listed on IDEAS

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    1. Qin, Yang & Zhong, Xiaoxiong & Jiang, Hao & Ye, Yibin, 2015. "An environment aware epidemic spreading model and immune strategy in complex networks," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 206-215.
    2. Pu, Cunlai & Li, Siyuan & Yang, XianXia & Xu, Zhongqi & Ji, Zexuan & Yang, Jian, 2016. "Traffic-driven SIR epidemic spreading in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 129-137.
    3. Pu, Cunlai & Li, Siyuan & Yang, Jian, 2015. "Epidemic spreading driven by biased random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 230-239.
    4. Pu, Cun-Lai & Pei, Wen-Jiang & Michaelson, Andrew, 2012. "Robustness analysis of network controllability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4420-4425.
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    1. Schaum, A. & Bernal-Jaquez, R. & Alarcon Ramos, L., 2022. "Data-assimilation and state estimation for contact-based spreading processes using the ensemble kalman filter: Application to COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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