Geodesic
A continuous-discrete model of the spread and control of tuberculosis
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 86-97.

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The equations of a continuous-discrete mathematical model of the spread and control of tuberculosis in a certain region are presented. The equations of the model are constructed that account for the reproduction of the population of the region and impulse changes in the numbers of individuals at discrete points in time under the influence of various factors. The results of the investigations of solutions to the model are formulated. The conditions are obtained on the parameters of the model and the initial data under which there exist solutions to the model interpreted as the complete extinction of tuberculosis in a region or the maintenance of the sizes of groups of infected individuals at a certain acceptable level. For analyzing the solutions to the model, we use the method of monotone operators and a comparison system in the form of delay integrodifferential equations, which is a simplified version of the original model.
Keywords: delay integrodifferential equation, asymptotic behavior of solutions, method of monotone operators, epidemiology, tuberculosis. 
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N. V. Pertsev. A continuous-discrete model of the spread and control of tuberculosis. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 86-97. http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a8/

[1] Perelman M. I., Marchuk G. I., Borisov S. E., Kazennykh B. Ya., Avilov K. K., Karkach A. S., Romanyukha A. A., “Tuberculosis epidemiology in Russia: the mathematical model and data analysis”, Russ. J. Numer. Anal. Math. Modelling, 19:4 (2004), 305–314 | DOI | MR | Zbl

[2] Avilov K. K., Romanyukha A. A., “Mathematical modelling of tuberculosis propagation and patient dtection”, Automat. Remote Control, 68:9 (2007), 1604–1617 | DOI | MR | Zbl

[3] Melnichenko A. O., Romanyukha A. A., “A model of tuberculosis epidemiology: estimation of parameters and analysis of factors influencing the dynamics of an epidemic process”, Russ. J. Numer. Anal. Math. Modelling, 23:1 (2008), 1–13 | DOI | MR

[4] Melnichenko O. A., “Sravnenie programm kontrolya tuberkuleza s pomoschyu matematicheskoi modeli epidemicheskogo protsessa”, Matematicheskaya biologiya i bioinformatika, Dokl. 3 Mezhdunar. konf. (g. Puschino, 10–15 oktyabrya 2010 g.), Maks Press, M., 2010, 254–255

[5] Avilov K. K., “Vliyanie sotsioekonomicheskikh faktorov na vyyavlenie bolnykh tuberkulezom”, Matematicheskaya biologiya i bioinformatika, Dokl. 3 Mezhdunar. konf. (g. Puschino, 10–15 oktyabrya 2010 g.), Maks Press, M., 2010, 256–257

[6] Pertsev N. V., Pichugin B. Yu., Pichugina A. N., “Issledovanie asimptoticheskogo povedeniya reshenii nekotorykh modelei epidemicheskikh protsessov”, Mat. biologiya i bioinformatika, 8:1 (2013), 21–48

[7] Kolmanovskii V. B., Nosov V. R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981 | MR

[8] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962 | MR

[9] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[10] Pertsev N. V., “Primenenie monotonnogo metoda i $M$-matrits k analizu povedeniya reshenii nekotorykh modelei biologicheskikh protsessov”, Sib. zhurn. industr. matematiki, 5:4(12) (2002), 110–122 | MR | Zbl