Kalman filter based on a fractional discrete-time stochastic augmented CoVid-19 model  

作　　者：Mohammad Ghani Dwi Rantini Maryamah 

机构地区：[1]Data Science Technology,Faculty of Advanced Technology and Multidiscipline,Universitas Airlangga,Surabaya 60115,Indonesia

出　　处：《Journal of Biosafety and Biosecurity》2024年第2期76-98,共23页生物安全和生物安保杂志（英文）

基　　金：financial support for the research under contract number 121/UN3.1.17/PT/2022 from the Faculty of Advanced Technology and Multidiscipline,Universitas Airlangga,Indonesia.

摘　　要：In this paper,we study the dynamics of the CoVid-19 outbreak in Semarang,Indonesia,using a fractional CoVid-19 model.We first determine the effects of the isolation rateand infection rate b on the reproduction number R0 and infected number V.We find that R0 is directly proportional to b and inversely proportional to.For V,the effect of physical distancing is not as significant as changing.Asincreases,V decreases,the number of susceptible individuals increases,the number of quarantined individuals decreases sharply,and the number of recovered individuals decreases.Moreover,the effect of vaccination is also considered.The combination of physical distancing,isolation,and vaccination has a significant impact on reducing the number of infected individuals.Analysis of dynamical systems allows us to understand the characteristics of our model,such as its boundedness and non-negativity,the existence of equilibrium points,the existence and uniqueness of solutions,and the local and global stability.To validate our fractional CoVid-19 model,we introduce the fractional extended Kalman filter(FracEKF)as a prediction method and compare the results against reported CoVid-19 data.FracEKF is a modified version of the basic extended Kalman filter with a time-fractional memory effect.The prediction results illustrate the accuracy of this model in terms of the root mean square error(RMSE),normalized root mean square error(NRMSE),and mean absolute percentage error(MAPE)for each fractional-order.Varyingreproduces the trends observed in the reported data for the number of infected individuals,i.e.,whenincreases,the infected number decreases.Moreover,a higher fractional-order results in higher model accuracy.Furthermore,higher values of the process noise Qf give smaller errors,whereas higher values of the observation noise Rf produce higher errors.Qf and the fractional-order a are inversely proportional to RMSE;NRMSE,and MAPE,whereas Rf is directly proportional to RMSE;NRMSE,and MAPE.

关 键 词：stability. FRACTIONAL INVERSE 

分 类 号：R563.1[医药卫生—呼吸系统]