Geodesic
SIRV-D optimal control model for COVID-19 propagation scenarios
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 87-97.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article presents the compartmental differential formulation of SIR-type for modeling the dynamics of the incidence of viral infections, in particular COVID-19, taking into account the ongoing vaccination campaign and the possibility of losing immunity during some time period after vaccination or a disease. The proposed model is extended by considering the coefficients of the model as dependent on the social loyalty of the population to isolation and vaccination. This allows us to formulate the optimal control problem and build various scenarios for the development of the epidemiological situation. The results obtained on the basis of the considered models were compared with real statistical data on the incidence in the Krasnoyarsk Territory.
Keywords: scenarios of COVID-19 propagation, SIR-type model, optimal control model. 
@article{JSFU_2023_16_1_a8,
     author = {Viktoriya S. Petrakova and Vladimir V. Shaidurov},
     title = {SIRV-D optimal control model for {COVID-19} propagation scenarios},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {87--97},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a8/}
}
TY  - JOUR
AU  - Viktoriya S. Petrakova
AU  - Vladimir V. Shaidurov
TI  - SIRV-D optimal control model for COVID-19 propagation scenarios
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2023
SP  - 87
EP  - 97
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a8/
LA  - en
ID  - JSFU_2023_16_1_a8
ER  - 
%0 Journal Article
%A Viktoriya S. Petrakova
%A Vladimir V. Shaidurov
%T SIRV-D optimal control model for COVID-19 propagation scenarios
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2023
%P 87-97
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a8/
%G en
%F JSFU_2023_16_1_a8
Viktoriya S. Petrakova; Vladimir V. Shaidurov. SIRV-D optimal control model for COVID-19 propagation scenarios. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 87-97. http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a8/

[1] D.Rafiq, A.Batool, M. Bazaz, “Three months of COVID-19: a systematic review and meta-analysis”, Rev. Med. Virol., 30:4 (2020), e2113 | DOI

[2] W.O.Kermack, A.G.McKendrick, “A contribution to the mathematical theory of epidemics”, Proc. R. Soc. Lond. Ser. A, Contain. Pap. Math. Phys. Character, 115 (1927), 700–721

[3] O.I.Krivorotko, S.I.Kabanikhin, Mathematical models of COVID-19 spread, 2021, 700–721, arXiv: 2112.05315

[4] H.Mohammadi, S.Rezapour, A.Jajarmi, “On the Fractional SIRD Mathematical Model and Control for the Transmission of COVID-19: the First and the Second Waves of the Disease in Iran and Japan”, ISA Transactions, 124 (2021), 103–114 | DOI

[5] S.B.Ramezani, A Amirlatifi, S.Rahimi, “A novel compartmental model to capture the nonlinear trend of COVID-19”, Comput. Biol. Med., 134 (2021), 104421 | DOI

[6] O.I.Krivorotko, S.I.Kabanikhin, N.Y.Zyatkov et al., “Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region”, Numer. Analys. Appl., 13 (2020), 332–348

[7] F.Brauer, P.Driessche, J.Wu, “Mathematical Epidemiology”, Lecture Notes in Mathematics, 355, 2008, 412

[8] T.T.Marinov, R.S.Marinova, “Dynamics of COVID-19 using inverse problem for coefficient identification in SIR epidemic models”, Chaos, Solitons and Fractals, 5 (2020), 100041 | DOI

[9] A.Cintroń-Arias, H.T.Banks, A.Capaldi, A.L.Lloyd, “A sensitivity matrix based methodology for inverse problem formulation”, Journal of Inverse and Ill-Posed Problems, 17:6 (2009), 1–20 | DOI

[10] A.Paticchio, T. Scarlatti, et al., Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread, 2020, arXiv: 2010.05074v1 [cs.LG]

[11] (Last access - 05/21/2022) https://ngs24.ru/text/health/2021/09/23/70151987/

[12] A.D.Lewis, The Maximum Principle of Pontryaginin control and in optimal control, Interim Reportson work of the International Institute for Applied Systems Analysis, 143, 2006