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.

Department of Electrical Engineering Indian Institute of Technology Indore Indore India

Faculty of Informatics and Management University of Hradec Kralove Czech Republic

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Cascella M., Rajnik M., Cuomo, et al. Features, evaluation and treatment coronavirus covid-19. Statpearls [Internet] 2020 PubMed

Zhang T., Wu Q., Zhang Z. Probable pangolin origin of SARS-CoV-2 associated with the covid-19 outbreak. Curr. Biol. 2020;30(7):1346–1351. PubMed PMC

MultiMedia LLC T. 2021. Covid-19 coronavirus pandemic. URL https://www.worldometers.info/coronavirus/

Mygov T. 2021. Covid-19 coronavirus pandemic. URL https://www.mygov.in/covid-19/?cbps=1/

Suthar S., Das S., Nagpure Z., et al. Epidemiology and diagnosis, environmental resources quality and socio-economic perspectives for COVID-19 pandemic. J. Environ. Manag. 2021;280 PubMed PMC

Chaudhary P.K., Pachori R.B. FBSED based automatic diagnosis of covid-19 using X-ray and CT images. Comput. Biol. Med. 2021;134 PubMed PMC

Bhattacharyya A., Bhaik D., et al. A deep learning based approach for automatic detection of COVID-19 cases using chest X-ray images. Biomed. Sig. Proc. Cont. 2022;71 PubMed PMC

Di Giamberardino P., Iacoviello D. Evaluation of the effect of different policies in the containment of epidemic spreads for the covid-19 case. Biomed. Sig. Proc. Cont. 2021;65:102325. PubMed PMC

Briat C., Verriest E.I. A new delay-SIR model for pulse vaccination. Biomed. Sig. Proc. Cont. 2009;4(4):272–277.

Treesatayapun C. Epidemic model dynamics and fuzzy neural-network optimal control with impulsive traveling and migrating: Case study of covid-19 vaccination. Biomed. Sig. Proc. Cont. 2022;71 PubMed PMC

Bhatia V., Mitra R. Signal processing based predictor for covid-19 cases. ResearchGate. 2020 doi: 10.13140/RG.2.2.23431.55201. DOI

Lahrouz A., Omari L., et al. Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model. Nonlinear Anal.: Model Control. 2011;16(1):59–76.

Gatto M., Bertuzzo E., et al. Spread and dynamics of the covid-19 epidemic in Italy: Effects of emergency containment measures. Proc. Natl. Acad. Sci. 2020;117(19):10484–10491. PubMed PMC

Kabir K.A., Kuga K., Tanimoto J. Analysis of SIR epidemic model with information spreading of awareness. Chaos Solitons Fractals. 2019;119:118–125.

Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A Math. Phys. 1927;115(772):700–721.

Hasan A., Susanto H., et al. A new estimation method for covid-19 time-varying reproduction number using active cases. Sci. Rep. 2022;12(1):1–9. PubMed PMC

Islam M.S., Hoque M.E., Amin M.R. Integration of Kalman filter in the epidemiological model: a robust approach to predict covid-19 outbreak in Bangladesh. Internat. J. Modern Phys. C. 2021;32(08)

Bootsma M.C., Ferguson N.M. The effect of public health measures on the 1918 Influenza pandemic in US cities. Proc. Natl. Acad. Sci. 2007;104(18):7588–7593. PubMed PMC

Sidi Ammi M., Tahiri M. Analysis of Infectious Disease Problems (Covid-19) and their Global Impact. Springer; 2021. Study of transmission dynamics of covid-19 virus using fractional model: case of Morocco; pp. 617–627.

Sameni R. 2020. Mathematical modeling of epidemic diseases; a case study of the covid-19 coronavirus. arXiv preprint arXiv:2003.11371.

Yang W., Sun C., Arino J. Global analysis for a general epidemiological model with vaccination and varying population. J. Math. Anal. Appl. 2010;372(1):208–223.

Parolini N., Ardenghi G., Quarteroni A., et al. Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model. Infect. Dis. Model. 2022;7(2):45–63. PubMed PMC

Song J., Xie H., Gao B., Zhong Y., Gu C., Choi K.-S. Maximum likelihood-based extended Kalman filter for covid-19 prediction. Chaos Solitons Fractals. 2021;146 PubMed PMC

Zhu X., Gao B., Zhong Y., et al. Extended Kalman filter based on stochastic epidemiological model for covid-19 modelling. Comput. Biol. Med. 2021;137:104810. PubMed PMC

Giordano G., Colaneri M., Di Filippo A., et al. Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy. Nature Med. 2021;27(6):993–998. PubMed PMC

Ferguson N.M., Donnelly C.A., Anderson R.M. The foot-and-mouth epidemic in great britain: pattern of spread and impact of interventions. Sci. J. 2001;292(5519):1155–1160. PubMed

Moore S., Hill E.M., Tildesley M.J., Dyson L., Keeling M.J. Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study. Lancet Infect. Dis. 2021;21(6):793–802. PubMed PMC

Trawicki M.B. Deterministic SEIRs epidemic model for modeling vital dynamics, vaccinations, and temporary immunity. Math. 2017;5(1):7.

Arino J., Van Den Driessche P. Positive Systems. Springer; 2003. The basic reproduction number in a multi-city compartmental epidemic model; pp. 135–142.

Golechha M. Covid-19 containment in Asia’s largest Urban Slum Dharavi-Mumbai, India: Lessons for policy-makers globally. J. Urban Health. 2020;97(6):796–801. PubMed PMC

Wheatley A.K., Juno P., et al. Evolution of immune responses to SARS-CoV-2 in mild-moderate covid-19. Nat. Comm. 2021;12(1):1–11. PubMed PMC

Arevalo-Rodriguez I., Buitrago P., et al. False-negative results of initial RT-PCR assays for covid-19: a systematic review. PLoS One. 2020;15(12):E0242958. PubMed PMC

Singh U.K., Singh A.K., et al. EKF and UKF based estimators for radar system. Front. Sig. Proc. 2021;1:5.

Oke M., Ogunmiloro O., et al. Mathematical modeling and stability analysis of a SIRV epidemic model with non-linear force of infection and treatment. Commun. Math. Appl. 2019;10(4):717–731.

Khajanchi S., Bera S., Roy T.K. Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes. Math. Comput. Simul. 2021;180:354–378.

Bera S., Khajanchi S., Roy T.K. Dynamics of an HTLV-I infection model with delayed CTLs immune response. Appl. Math. Comput. 2022;430

Ottaviano S., Sensi M., Sottile S. Global stability of SAIRS epidemic models. Nonlinear Anal. RWA. 2022;65

Arasaratnam I., Haykin S., Hurd T.R. Cubature Kalman filtering for continuous-discrete systems: theory and simulations. IEEE Trans. Signal Proces. 2010;58(10):4977–4993.

Arasaratnam I., Haykin S. Cubature Kalman filters. IEEE Trans. Automat. Control. 2009;54(6):1254–1269.

Nanda S.K., Bhatia V., Singh A.K. Performance analysis of Cubature rule based Kalman filter for target tracking. 2020 IEEE 17th India Counc. Int. Conf.; INDICON; IEEE; 2020. pp. 1–6.

Särkkä S., Sarmavuori J. Gaussian filtering and smoothing for continuous-discrete dynamic systems. Signal Proces. 2013;93(2):500–510.

Bhaumik S., Date P. CRC Press; 2019. Nonlinear Estimation: Methods and Applications with Deterministic Sample Points.

Singh A.K., Bhaumik S. Higher degree cubature quadrature Kalman filter. Int. J. Cont. Autom. Syst. 2015;13(5):1097–1105.

Stroud A. Approximate Calculation of Multiple Integrals. Prentice-Hall, Inc.; Englewood Cliffs, NJ: 1971. (Prentice-Hall Ser. in Auto. Comp.).

Bhaumik S. Cubature quadrature Kalman filter. IET Sig. Proc. 2013;7(7):533–541.

Li S., Xu B., et al. Improved maximum correntropy cubature Kalman filter for cooperative localization. IEEE Sens. J. 2020;20(22):13585–13595.