Bansal Rahul, Kumar Amit, Singh Amit Kumar, Kumar Sandeep
ECE Department, Ajay Kumar Garg Engineering College, Ghaziabad, India.
CS Department, Dyal Singh College, University of Delhi, Delhi, India.
Digit Signal Process. 2021 May;112:103001. doi: 10.1016/j.dsp.2021.103001. Epub 2021 Feb 15.
In this study, the transmissibility estimation of novel coronavirus (COVID-19) has been presented using the generalized fractional-order calculus (FOC) based extended Kalman filter (EKF) and wavelet transform (WT) methods. Initially, the state-space representation for the bats-hosts-reservoir-people (BHRP) model is obtained using a set of fractional order differential equations for the susceptible-exposed-infectious-recovered (SEIR) model. Afterward, the EKF and Kronecker product based WT methods have been applied to the discrete vector representation of the BHRP model. The main advantage of using EKF in this system is that it considers both the process and the measurement noise, which gives better accuracy and probable states, which are the Markovian (processes). The importance of proposed models lies in the fact that these models can accommodate conventional EKF and WT methods as their special cases. Further, we have compared the estimated number of contagious people and recovered people with the actual number of infectious people and recovered people in India and China.
在本研究中，使用基于广义分数阶微积分（FOC）的扩展卡尔曼滤波器（EKF）和小波变换（WT）方法对新型冠状病毒（COVID - 19）的传播性进行了估计。首先，通过一组针对易感 - 暴露 - 感染 - 康复（SEIR）模型的分数阶微分方程，获得了蝙蝠 - 宿主 - 蓄水池 - 人群（BHRP）模型的状态空间表示。随后，将基于EKF和克罗内克积的WT方法应用于BHRP模型的离散向量表示。在该系统中使用EKF的主要优点在于它同时考虑了过程噪声和测量噪声，从而能给出更好的精度和可能状态，这些状态是马尔可夫（过程）。所提出模型的重要性在于这些模型可以将传统的EKF和WT方法作为其特殊情况包含在内。此外，我们还将印度和中国的传染性人群和康复人群的估计数量与实际感染人群和康复人群数量进行了比较。
