Geodesic
Development of mathematical epidemic models taking into account the effects of isolating individuals in a population
Matematičeskoe modelirovanie, Tome 33 (2021) no. 11, pp. 39-60.

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

The paper analyzes the effect of isolation of individuals of the population on the dynamics of the epidemic. Based on the SIR model, a SIRDi model was built, which takes into account the isolation of individuals, as well as the presence of deceased patients, which is appropriate to use in cases of extensive spread of infection, when the number of infected is comparable to the number of susceptible (i.e., those who can be infected). Simplified IRD and IRDi models are proposed for studying the spread of an infectious disease at the initial stage of an epidemic (or for the case when the infection rate is not high). It was found that there is a threshold value of the isolation coefficient (fraction), which delimits the qualitatively different behavior of the epidemic indicators of a system. A comparison is made between different models. It is shown that the simplified (IRDi) and more complete (SIRDi) models at the initial stage of the epidemic give approximately the same results.
Keywords: epidemic, reproduction numbers, SIR model
Mots-clés : isolation coefficient. 
@article{MM_2021_33_11_a2,
     author = {T. R. Amanbaev and S. J. Antony},
     title = {Development of mathematical epidemic models taking into account the effects of isolating individuals in a population},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {39--60},
     publisher = {mathdoc},
     volume = {33},
     number = {11},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_11_a2/}
}
TY  - JOUR
AU  - T. R. Amanbaev
AU  - S. J. Antony
TI  - Development of mathematical epidemic models taking into account the effects of isolating individuals in a population
JO  - Matematičeskoe modelirovanie
PY  - 2021
SP  - 39
EP  - 60
VL  - 33
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2021_33_11_a2/
LA  - ru
ID  - MM_2021_33_11_a2
ER  - 
%0 Journal Article
%A T. R. Amanbaev
%A S. J. Antony
%T Development of mathematical epidemic models taking into account the effects of isolating individuals in a population
%J Matematičeskoe modelirovanie
%D 2021
%P 39-60
%V 33
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2021_33_11_a2/
%G ru
%F MM_2021_33_11_a2
T. R. Amanbaev; S. J. Antony. Development of mathematical epidemic models taking into account the effects of isolating individuals in a population. Matematičeskoe modelirovanie, Tome 33 (2021) no. 11, pp. 39-60. http://geodesic.mathdoc.fr/item/MM_2021_33_11_a2/

[1] V. Volterra, “Fluctuations in the abundance of a species considered mathematically”, Nature, 118 (1926), 558–560 | DOI | Zbl

[2] A. J. Lotka, Elements of Physical Biology, Nature, 116, 1925, 461 pp. | DOI

[3] H. Weiss, “The SIR model and the foundations of public health”, Materials Mathematics, 3 (2013), 17 pp.

[4] R. M. Anderson, “Discussion: the Kermack-McKendrick epidemic threshold theorem”, Bulletin of Mathematical Biology, 53:1 (1991), 1–12 | DOI

[5] O. N. Bjornstad, K. Shea, M. Krzywinski, N. Altman, “Modeling infectious epidemics”, Nature methods, 17 (2020), 455–456 | DOI

[6] M. Mandal, S. Jana, S. K. Nandi, A. Khatua, S. Adak, T. K. Kar, “A model based study on the dynamics of COVID-19: Prediction and control”, Chaos, Solitons and Fractals, 136 (2020), 109889 | DOI

[7] M. J. Keeling, P. Rohani, Modelling Infectious Diseases in Humans and Animals, Princeton University Press, New Jersey, 2008, 384 pp.

[8] R. E. Baker, W. Yang, G. A. Vecchi, C. J. Metcalf, B. Greenfell, “Susceptible supply limits the role of climate in the early SARS-CoV-2 pandemic”, Science | DOI

[9] U. Ledzewicz, H. Schattler, “On optimal singular controls for a general SIR-model with vaccination and treatment”, Discrete and Continuous Dynamic. Systems, 2 (2011), 981–990

[10] A. A. Romaniukha, Matematicheskie modeli v immunologii i epidemiologii infektsionnykh zabolevanii, Izd-vo Binom, M., 2011, 285 pp.

[11] G. I. Marchuk, Matematicheskie modeli v immunologii. Vychislitelnye metody i eksperimenty, Nauka, M., 1991, 304 pp.

[12] Y. Liu, Y. Zhao, “The spread behavior analysis of a SIQR epidemic model under the small world network environment”, IOP Conf. Series: Journal of Physics. Conf. Series, 1267 (2019), 012042 | DOI

[13] T. Odagaki, “Exact properties of SIQR model for COVID-19”, Physica A, 564 (2021), 125564 | DOI

[14] L. Zhong, L. Mu, J. Li, J. Wang, Z. Yin, D. Liu, “Early prediction of the 2019 novel coronavirus outbreak in the mainland China based on simple mathematical model”, IEEE Access, 8 (2020), 51761–51768 | DOI

[15] A. I. Shnip, “Kineticheskaia model dinamiki epidemii i ee testirovanie na dannykh rasprostraneniia epidemii COVID-19”, Inzh. fizich. zhurnal, 94:1 (2021), 9–21

[16] I. V. Derevich, A. A. Panova, “Raschet skorosti infitsirovaniia COVID-19 na osnove metoda pogruzheniia”, Inzhenerno-fizicheskii zhurnal, 94:1 (2021), 22–34

[17] H. Hethcote, “The Mathematics of Infectious Diseases”, SIAM Review, 42 (2000), 599–653 | DOI | Zbl

[18] C. Dye, “Epidemiology: Modeling the SARS Epidemic”, Science, 300 (2003), 1884–1885 | DOI

[19] J. Koopman, “Modeling infection transmission”, Annu. Rev. Public Health, 25 (2004), 303–326 | DOI

[20] J. H. Jones, Notes on $R_0$, Stanford university, Stanford, 2007, 19 pp.

[21] P. V. Driessche, J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission”, Math Biosci., 180 (2002), 29–48 | DOI | Zbl

[22] S. Zhao, J. Ran, S. S. Musa et al, “Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: a data-driven analysis in the early phase of the outbreak”, Int. J. Infect. Dis., 92 (2020), 214–217 | DOI

[23] R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991, 757 pp.