Knowing the parameters of the infectious and epidemic process allows us to make a forecast and calculate the amount of exposure to infectious morbidity. On the basis of real data of registered cases of the disease, mathematical modelling of serial morbidity increases was carried out. The parameters and initial conditions of five viral infections (mumps, chickenpox, rubella, measles and viral hepatitis A) were determined. The reproductive number ranged at 2.4–5.3, while the oscillation amplitudes were targeted at 0.10–0.57. The non-linear incidence rate coefficient ranged at 0–0.012. These parameters determine the individual profile of the infection in a particular territory. The cyclicity and seasonality of infections were then also studied. The study has shown that the mechanism of the epidemic process development is the imposition of seasonal fluctuations of the frequency of contacts on the natural frequency of the system oscillation. The duration of the infectious process is directly proportional to the value of the natural period of the system oscillation. Mathematical modelling using information technologies makes it possible to predict the morbidity dynamics and determine the value of measures to reduce it.
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2. Anderson R, Mej R. Infekcionnye bolezni cheloveka. Dinamika i ko ntrol ’. 2004. 782 p. (In Russ).
3. Berhe HW, Makinde OD. Computational modelling and optimal control of measles epidemic in human population. Biosystems. 2020; 190: 104102.
4. Campbell F, Archer B, Laurenson -Schafer H, Jinnai Y, Konings F, Batra N, et al. Increased transmissibility and global spread of SARS-CoV-2 variants of concern as at June 2021. Eurosurveillance. 2021; 26(24): 2100509.
5. Rodriguez LL, Roo ADe, Guimard Y, Trappier SG, Sanchez A, Bressler D, et al. Persistence and genetic stability of Ebola virus during the outbreak in Kikwit , Democratic Republic of the Congo, 1995. The Journal of infectious diseases. 1999; 179(1): 170-176.
6. Gerasimov AN. Modeli i statisticheskij analiz v epidemiologii infekcionnyh zabolevanij. Tihookeanskij medicinskij zhurnal. 2019; 3(77): 80-83. ( In Russ ).
7. Karkach AS , Romanyuha AA. Sovremennye podhody k analizu i prognozirovaniyu zdorov ’ ya naseleniya s pomoshch ’ yu matematicheskih modelej. Vrach i informacionnye tekhnologii. 2014; 1: 38-47. ( In Russ ).
8. Brazhnikov AY u , Gerasimov AN. Opyt primeneniya korrelyacionnogo analiza dlya ocenki izucheniya sinhronnosti kolebanij urovnya infekcionnoj zabolevaemosti na otdel ’ nyh territoriyah. Z h urnal mikrobiologii , epidemiologii i immunologii. 1999; 4: 1-5. ( In Russ ).
9. Gusev AV , Novickij RE. Tekhnologii prognoznoj analitiki v bor ’ be s pandemiej COVID -19. Vrach i informacionnye tekhnolo gii. 2020; 4: 24-33. (In Russ).
10. Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proceedings of the royal society of London. Series A, Containing papers of a mathematical and physical character. 1927 ; 115 (772): 700-721.
11. Gasnikov AV. Sovremennye chislennye metody optimizacii. Metod universal ’ nogo gradientnogo spuska : uchebnoe posobie. M.: MFTI, 2018. 291 р. Izd. 2-e, dop. (In Russ ).
12. Heymann DL. Control of communicable diseases manual. American Public Health Association. 2008; 19: 746 p.
13. Y u shchuk ND. Infekcionnye bolezni : nacional ’ noe rukovodstvo. N. D. Y u shchuk , Y u. Y a. Vengerov , editors. M.: GEOTAR-Media, 2019. 1047 р. (In Russ).
14. Korobeinikov A, Maini PK. Non-linear incidence and stability of infectious disease models. Mathematical medicine and biology: a journal of the IMA. 2005; 22(2): 113-128.
15. Liu W, Levin SA, Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. Journal of mathematical biology. 1986; 23(2): 187-204.
16. Rohith G, Devika KB. Dynamics and control of COVID-19 pandemic with nonlinear incidence rates. Nonlinear Dynamics. 2020; 101(3): 2013-2026.
17. Belyakov VD. Samoregulyaciya parazitarnyh sistem i mekhanizm razvitiya epidemicheskogo processa. Vestnik Akademii medicinskih nauk SSSR. 1983; 5: 3-9. ( In Russ ).
18. Romanyuha AA. Matematicheskie modeli v immunologii i epidemiologii infekcionnyh zabolevanij. M.: Binom. Laboratoriya znanij , 2012. 293 р. (In Russ).
19. Cauchemez S, Ferguson NM. Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London. Journal of the Royal Society Interface. 2008 ; 5 ( 25 ): 885 - 897.
For citation
Semenova D.A., Prostov M.Y., Zarubina T.V., Veselova E.I., Vinokurov A.S., Zatsepin O.V., Karamov E.V., Lagutkin D.A., Lebedev S.N., Lomovtsev A.E., Panova A.E., Prostov Y.I., Turgiev A.S., Chernetsova V.V., Kaminskiy G.D. Mathematical modeling of recurrent epidemics of viral infections on the data of the town of the Russian Federation. Medical doctor and information technology. 2021; 3: 84-95. (In Russ.). doi : 1025881/18110193_2021_3_84.
Keywords