The practicality of administrative measures for covid-19 prevention is crucially based on quantitative information 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 S I R family. The fundamental S I R model consists of S-susceptible, I-infected, and R-recovered from infected compartmental populations. To obtain the desired quantitative information, 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 S E I R R P V model, which, in addition to the S and I populations, consists of the E-exposed, R e-recovered from exposed, R-recovered from infected, P-passed away, and V-vaccinated populations. Availing of this additional information, the proposed S E I R R P V model helps in further strengthening the practicality of the administrative measures. The proposed S E I R R P V 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 S E I R R P V 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 S E I R R P V model. Finally, the performance of the proposed S E I R R P V model is validated for real-data of covid-19 outbreak.