Kalman-based compartmental estimation for covid-19 pandemic using advanced epidemic model

The practicality of administrative measures for covid-19 prevention is crucially based on quantitative in-formation on impacts of various covid-19 transmission influencing elements, including social distancing, contact tracing, medical facilities, vaccine inoculation, etc. A scientific approach of obtaining such quantitative information is based on epidemic models of SIR family. The fundamental SIR model consists of S-susceptible, I-infected, and R-recovered from infected compartmental populations. To obtain the desired quantitative infor-mation, these compartmental populations are estimated for varying metaphoric parametric values of various transmission influencing elements, as mentioned above. This paper introduces a new model, named SEIRRPV model, which, in addition to the S and I populations, consists of the E-exposed, Re-recovered from exposed, R-recovered from infected, P-passed away, and V-vaccinated populations. Availing of this additional information, the proposed SEIRRPV model helps in further strengthening the practicality of the administrative measures. The proposed SEIRRPV model is nonlinear and stochastic, requiring a nonlinear estimator to obtain the compartmental populations. This paper uses cubature Kalman filter (CKF) for the nonlinear estimation, which is known for providing an appreciably good accuracy at a fairly small computational demand. The proposed SEIRRPV model, for the first time, stochastically considers the exposed, infected, and vaccinated populations in a single model. The paper also analyzes the non-negativity, epidemic equilibrium, uniqueness, boundary condition, reproduction rate, sensitivity, and local and global stability in disease-free and endemic conditions for the proposed SEIRRPV model. Finally, the performance of the proposed SEIRRPV model is validated for real-data of covid-19 outbreak.