Vestnik On-line
Orenburg State University november 30, 2021   RU/EN
Headings of Vestnik
Pedagogics
Psychology
Other

Search
Vak
Антиплагиат
Orcid
Viniti
ЭБС Лань
Rsl
Лицензия Creative Commons

2010, № 9



Bolodurina I.P., Lugovskova Y.P. THE SIMULATION OF THE STOCHASTIC FLUCTUATIONS OF THE NONLINEAR SYSTEM OF THE DIFFERENTIAL EQUATIONS, DESCRIBING THE DYNAMICS OF IMMUNE RESPONSE WITH THE INFECTIOUS DISEASESThe work represents the results of the program realization of the numerical algorithm of the solution of the stochastic differential equations, describing the dynamics of the development of infectious diseases at the cellular level, based on the standardized decomposition by Taylor — Ito in terms of the repeated stochastic integrals with their subsequent approximation with help of the polynomial set of functions. Key words: immune response, stochastic model, the mathematical simulation.

Download
References:

1. Burnet, F. Cellular Immunology / FM Burnet. — Moscow: Mir, 1971. — 544.

2. White, LN Analysis of mathematical models in immunology / LN White, GI Marchuk. — Moscow: Nauka, 1988. — 192.

3. Bolodurina, IP A stochastic model of the dynamics of infectious diseases under the influence of random perturbations / IP Bolodurina, JP Lugovskova / / Technology in the XXI Century: Current Status and Prospects of Development: Monograph. — Book 4. — Novosibirsk: TSRNS, 2009. — 286.

4. Bolodurina, IP Stochastic model of infectious diseases, based on the principles of the immune system / IP Bolodurina, JP Lugovskova / / Review of Applied and Industrial Mathematics. 2009. T. 16. Vol. 6. S. 1028-1029.

5. Volkov, IK Random Processes: Textbook for Universities / IK Volkov, SM Zuev, GM Tsvetkova .- M.: MSTU them. NE Bauman, 2006. — 448.

6. Gikhman, II Stochastic Differential Equations and Their Applications, II Gikhman, AV Walker. — Kiev: Naukova Dumka, 1982. — 612 sec.

7. Dasgupta, D. Artificial Immune Systems and Their Applications, D. Dasgupta. Trans. from English. Ed. AA Romanyukha. — M.: FIZMATLIT, 2006. — 344.

8. Kuznetsov, JF Numerical simulation of stochastic differential equations and stochastic integrals, DF Kuznetsov. — St. Petersburg: Nauka, 1999. — 459 sec.

9. Marchuk, GI Mathematical models in immunology / GI Marchuk. — Moscow: Nauka 1980. — 264 pp.

10. Rozov, AK Stochastic Differential Equations and Their Applications, AK Rozov. — St.: Polytechnic, 2005. — 303.


About this article

Authors: Lugovskova Yu.P., Bolodurina I.P.

Year: 2010


Editor-in-chief
Sergey Aleksandrovich
MIROSHNIKOV

Crossref
Cyberleninka
Doi
Europeanlibrary
Googleacademy
scienceindex
worldcat
© Электронное периодическое издание: ВЕСТНИК ОГУ on-line (VESTNIK OSU on-line), ISSN on-line 1814-6465
Зарегистрировано в Федеральной службе по надзору в сфере связи, информационных технологий и массовых коммуникаций
Свидетельство о регистрации СМИ: Эл № ФС77-37678 от 29 сентября 2009 г.
Учредитель: Оренбургский государственный университет (ОГУ)
Главный редактор: С.А. Мирошников
Адрес редакции: 460018, г. Оренбург, проспект Победы, д. 13, к. 2335
Тел./факс: (3532)37-27-78 E-mail: vestnik@mail.osu.ru
1999–2021 © CIT OSU