Russian version English version
Volume 20   Issue 2   Year 2025
References

  1. Verhulst P.F. Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique. 1838;10:113–121.
  2. McKendrick A.G., Pai M.K. XLV.–The Rate of Multiplication of Micro-organisms: A Mathematical Study. Proceedings of the Royal Society of Edinburgh. 1912;31:649–655. doi: 10.1017/S0370164600025426
  3. Pearl R., Reed L.J. On the Rate of Growth of the Population of the United States Since 1790 and its Mathematical Representation. PNAS. 1920;6:275–288. doi: 10.1073/pnas.6.6.275
  4. Pearl R. The Biology of Population Growth. New York: Alfred A. Knopf Inc., 1925: 260.
  5. Goldberg V.M. Development of chain models of the dynamics of the COVID-19 pandemic spread. Combustion and Explosion. 2021;14(3):3–10.
  6. Philippov A.A. Mathematical theory of epidemics and pandemics based on the laws of chain and thermal explosions. Doklady Physics. 2024;514(1). doi: 10.31857/S2686740024010061
  7. Saito T., Shigemoto K. A Logistic Curve in the SIR Model and Its Application to Deaths by COVID-19 in Japan. medRxiv. 2020. doi: 10.1101/2020.06.25.20139865v2
  8. Reiser P.A. Modified SIR Model Yielding a Logistic Solution. arXiv:2006.01550 [q-bio.PE]. doi: 10.48550/arXiv.2006.01550
  9. Semenov N.N. Tsepnye reaktsii (Chain reactions). Leningrad, 1934. 110 p. (in Russ.).
  10. Semenov N.N. In: Izbrannye trudy (Selected Works). Eds. Aldoshina S.M. et al. Vol. 1. Book 2. Moscow, 2004. P. 86 (in Russ.).
  11. Tselinskii I.V., Shugalei I.V., Lukogorskaia S.A. Chain processes in organic chemistry and biology. Rossiiskii Khimicheskii Zhurnal (Russian Chemistry Journal). 2001;45(2):35–45 (in Russ.).
  12. Zelʹdovich I.B. The Mathematical Theory of Combustion and Explosions. United Kingdom: Consultants Bureau, 1985. ISBN: 9780306109744.
  13. Philippov A.A., Berlin A.A. Mathematical theory of ignition by an incandescent surface. Doklady Physics. 2022;67(4):104-109. doi: 10.1134/S1028335822040024
  14. Kauffman S.A. Reinventing the Sacred: A New View of Science, Reason, and Religion: Basic Books. Chapter 5. 2008. P. 59–71.
  15. Knorre D.G. Physicochemical Biology: Conquered Boundaries and New Horizons. Acta Naturae. 2012;4(2):36–37 (in Russ.). doi: 10.32607/actanaturae.10624
  16. Astashina M.V., Zentsov V.N., Lapshakova I.V. Construction and industrial safety. 2022;25(77):95–102 (in Russ.).
  17. Dudarov S.P., Maklyaev I.V., Lemetyuynen Y.A., Guseva E.V., Karetkin B.A., Evdokimova S.A. Modeling biotechnological processes using a mathematical apparatus of artificial neural networks. Software & Systems. 2024;37(1):113–121. doi: 10.15827/0236-235X.142.113-121
  18. Oleskin A.V. Network Structures in Biological Systems. Biology Bulletin Reviews. 2014;4(1):47-70. doi: 10.1134/S2079086414010034
  19. Haydarova M., Haydarova O. Branching processes: theory, models and their application in biology, physics and computer science. Vestnik Nauki. 2024;3(5):1374–1378 (in Russ.).
  20. Vatutin V.A., D'yakonova E.E. Galton–Watson branching processes in a random environment. I: limit theorems. Theory Probab. Appl. 2004;48(2):314–336. doi: 10.1137/S0040585X97980373
  21. Kalinkin A.V. Markov branching processes with interaction. Russian Math. Surveys. 2002;57(2):241–304. doi: 10.1070/RM2002v057n02ABEH000496
  22. Ojeda G.B., Pardo J.P. Branching processes with pairwise interactions. ALEA. 2025;22:711–745. doi: 10.30757/ALEA.v22-28
  23. Mitrophanov A.Y. Markov-Chain Perturbation and Approximation Bounds in Stochastic Biochemical Kinetics. Mathematics. 2025;13(13). Article No. 2059. doi: 10.3390/math13132059
Table of Contents Original Article
Filippov A.A., Filippov-Kuznetsov R.A., Botin A.S. The Theory of Chain Processes in Biology and Sociology. Ìàthematical biology and bioinformatics. 2025;20(2):644-652. doi: 10.17537/2025.20.644
(published in Russian)

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