ENDEMIC EQUILIBRIUM IN THE EXTENDED SEIR MODEL
https://doi.org/10.56304/S2079562925020022
EDN: CUQQVM
Abstract
The paper discusses the formation of non-stationary, nonlinear states in an extended ER model of epidemic spread for a population of constant numbers under the assumption of equality of the rate of recovery and disease. The probabilities of transmission of infection, the characteristic times of disease development and recovery are also considered constant. The obtained analytical ratios are used to establish an acceptable range of control parameters that ensure the formation and existence of nonequilibrium distributions, which can be interpreted as a latent epidemiological phase.
About the Authors
A. R. Karimov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute);
Institute for High Temperatures, Russian Academy of Sciences
Russian Federation
Russian Federation
M. A. Solomatin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
References
1. Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology. 2012. New York: Springer. https://doi.org/10.1007/978-1-4614-1686-9
2. Li M.Y., Graef J.R., Wang L., Karsai J. // Math. Biosci. 1999. V. 160 (2). P. 191–213.
3. Hethcote H.W. // SIAM Rev. 2000. V. 42 (4). P. 599–653.
4. He S., Peng Y., Sun K. // Nonlinear Dyn. 2020. V. 101. P. 1667–1680.
5. Milgroom M.G. Biology of Infectious Disease: from Molecules to Ecosystems. 2023. Cham: Springer. P. 253–268.
6. Братусь А.С., Новожилов А.С., Платонов А.П. Динамические системы и модели биологии. 2010. Москва: Физматлит.
7. Авилов К.К., Романюха А.А. // Матем. биология и биоинформ. 2007. Т. 2 (2). С. 188–318.
8. Ojo M.M., Peter O.J., Goufo E.F.D., Panigoro H.S., and Oguntolu F.A. Mathematical model for control of tuberculosis epidemiology // J. Appl. Math. Comp. 2023. V. 69 (1). P. 69–87.
9. Igor D., Anastasiia P., Derevich I., Panova A. // Proc. Int. Work-Conf. Bioinformatics and Biomedical Engineering. 2023. Cham: Springer. P. 499–513.
10. Mwalili S., Kimathi M., Ojiambo V., Gathungu D., and Mbogo R. // BMC Res. Notes. 2020. V. 13 (1). P. 352.
11. Leonov A., Nagornov O., Tyuflin S. // Mathematics. 2022. V. 11 (1). P. 167.
12. Эмануэль Н.М., Кнорре Д.Г. Курс химической кинетики: Уч. для хим. фак. ун-тов. 4-е изд., перераб. и доп. 1984. Москва: Высш. шк.
13. Blumenfeld L.A. Problems of Biological Physics. 1981. Berlin: Springer.
14. Эльсгольц Л.Э. Дифференциальные уравнения и вариационное исчисление: Уч. для вузов. 1965. Москва: Наука.
15. Karimov A.R., Stenflo L., Yu M.Y. // Phys. Scr. 2022. V. 97 (8). P. 085007.
16. Каримов А.Р., Соломатин М.А. // Вестник НИЯУ МИФИ. 2024. Т. 13 (1). С. 30−39.
Review
For citations:
Karimov A.R., Solomatin M.A. ENDEMIC EQUILIBRIUM IN THE EXTENDED SEIR MODEL. Nuclear Physics and Engineering. 2025;16(2):254-258. (In Russ.) https://doi.org/10.56304/S2079562925020022. EDN: CUQQVM
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