Geodesic
Concept controlling model for arresting epidemics, including COVID-19
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 125-163

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Concept controlling model for arresting epidemics (further on - the model) of emerging, new and re-emerging infections has been developed. Epidemic force parameters are defined: high values of contact rate of infection in acute ($ R_1 $) and chronic ($ R_2 $) forms of disease, high frequency of chronization $\gamma_2 $ with pathogen excretion, high rate of loss of natural immunity $ k_1 $, high inflow of susceptible population $\mu $. Control targets have been identified: infected persons (detection, isolation and treatment $\delta $), transmission mechanism (regime-restrictive measures, sanitary and hygienic procedures $ r $), the decrease in susceptibility (vaccination, pre- and post-exposure prophylaxis $\lambda $). Critical interdependencies between epidemic force parameters and control coefficients were studied. We obtained threshold conditions for "zero infection" asymptotic stability. In order to achieve the target result more quickly, the use of "supercritical" control levels is proposed, with the model determining the time to achieve the result. The need to affect both acute and chronic forms of infection has been proven. The model allows to solve direct and inverse problems.
Keywords: control of communicable diseases, threshold, intervention campaign, parameters of the epidemic process, mathematical model. 
@article{SEMR_2024_21_1_a33,
     author = {G. D. Kaminskiy and Yu. I. Prostov and D. A. Semenova and M. Yu. Prostov and N. N. Pimenov and E. I. Veselova and A. S. Vinokurov and E. V. Karamov and A. E. Panova and A. S. Turgiev and V. V. Chernetsova and A. E. Lomovtsev},
     title = {Concept controlling model for arresting epidemics, including {COVID-19}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {125--163},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a33/}
}
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G. D. Kaminskiy; Yu. I. Prostov; D. A. Semenova; M. Yu. Prostov; N. N. Pimenov; E. I. Veselova; A. S. Vinokurov; E. V. Karamov; A. E. Panova; A. S. Turgiev; V. V. Chernetsova; A. E. Lomovtsev. Concept controlling model for arresting epidemics, including COVID-19. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 125-163. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a33/