Mathematical Modelling and Prediction in Infectious Disease Epidemiology

Cover Page

Abstract


Mathematical modeling of diseases is an urgent problem in the modern world. More and more researchers are turning to mathematical models to predict a particular disease, as they help the most correct and accurate study of changes in certain processes occurring in society. Mathematical modeling is indispensable in certain areas of medicine, where real experiments are impossible or difficult, for example, in epidemiology. The article is devoted to the historical aspects of studying the possibilities of mathematical modeling in medicine. The review demonstrates the main stages of development, achievements and prospects of this direction.


About the authors

E. Ya. Yanchevskaya

Astrakhan State Medical University

Author for correspondence.
Email: apteca-111a@mail.ru
Astrakhan, Russia

O. A. Mesnyankina

Astrakhan State Medical University

Email: apteca-111a@mail.ru
Astrakhan, Russia

References

  1. Uly`bin AV. A mathematical model of the spread of infection. Vestnik TGU. 2011. 16 (1): 184—187. (In Russ)
  2. Mezentseva LV, Pertsov SS. Mathematical modeling in Biomedicine. Vestnik novykh meditsinskikh tekhnologij. 2013. ХX (1): 11. (In Russ).
  3. Huppert G. Katriel Mathematical modelling and prediction in infectious disease epidemiology. Clinical Microbiology and Infection. 2013. 19 (11): 999—1005.
  4. Balanter BI, KHanin MА, CHernavskij DS. Introduction to mathematical modeling of pathological processes M.: Meditsina, 1980: 262 s. (In Russ)
  5. Merler S, Ajelli M, Pugliese A, Ferguson NM. Determinants of the spatiotemporal dynamics of the 2009 H1N1 pandemic in Europe: implications for real-time modelling. PLoS Comput Biol. 2011. 7( 9): e1002205.
  6. Pitzer VE, Atkins KE, de Blasio BF et al. Direct and indirect effects of rotavirus vaccination: comparing predictions from transmission dynamic models. PLoSONE. 2012. 7 (8): 42320.
  7. Yaari R, Katriel G, Huppert A, Axelsen J.B., Stone L. Modelling seasonal influenza: the role of weather and punctuated antigenic drift. J R Soc Interface 2013. 10: 20130298.
  8. Bernoulli D. Essai d’une nouvelle analyse de la mortalite causee par la petite verole. Mem Math Phy AcadRoy Sci Paris, 1766.
  9. Brownlee J. Statistical studies in immunity: the theory of an epidemic. Proceedings of the Royal Society of Edinburgh 26.1, 1906, 484—521.
  10. Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc R Soc Lond. 1927. 115:700—721.
  11. Lloyd AL. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theor Popul Biol. 2001. 60:59—71.
  12. Keeling MJ, Rohani P. Modeling infectious diseases in humans and animals. Princeton, Princeton University Press, 2008.
  13. Diekmann O, Heesterbeek H, Britton T. Mathematical tools for understanding infectious disease dynamics 2013. Princeton, Princeton University Press, 2013.
  14. Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford, Oxford University Press, 1992.
  15. Satorras R, Vespignani A. Epidemic spreading on scale-free networks. Phys Rev Lett. 2001. 86: 3200—3203.
  16. Belotserkovskij OM, KHolodov АS. Computer models and medical progress M.: Nauka, 2001. 300 s. (In Russ)
  17. Leonenko VN. Mathematical epidemiology: teaching manual for laboratory work. SPb.: Universitet ITMO, 2018: 38 s. (In Russ)
  18. En'ko PD. On the course of epidemics of some infectious diseases. Vrach. 1889. 46—48. (In Russ)
  19. Bartlett MS. An Introduction to Stochastic Processes, with special reference to methods and applications. Third edition. Cambridge University Press, 1978: 388.
  20. Bejli N. Mathematics in biology and medicine. M.: Mir, 1970: 327 s. (In Russ)
  21. Kendall DG. Discussion of ’Measles periodicity and community size’ by M.S. Bartlett. J Roy Stat Soc. Ser. A. 1957. 120: 64—76.
  22. Elveback L., Ackerman E., Gatewood L., Fox J. Stochastic two-agent epidemic simulation models for a community of families. American Journal of Epidemiology. 1971. 93: 267—280.
  23. May R.M. Uses and abuses of mathematics in biology. Science. 2004. 303: 790—793.

Statistics

Views

Abstract - 392

PDF (Russian) - 925

Cited-By


PlumX

Dimensions


Copyright (c) 2019 Yanchevskaya E.Y., Mesnyankina O.A.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies