Analytical solution and adaptation to the parameter estimation of the SIR model

Authors

  • S. M. Ivanov Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2020/4.6

Abstract

The article deals with analytical solution and adaptation to the parameter estimation of the SIR model of the epidemic. By a special replacement of the exponential function by inverse proportionality, the approximate general solution of the SIR model is found. It is spoken in detail about the process of integration of ordinary differential equations of the SIR model. The equality of the sum of the obtained analytical solutions and population size is checked. The obtained solutions are simple and understandable. To parametrically estimate the SIR model, its general solution is adapted to paired linear regressions. The article is of interest for students, graduate students and scientists involved in mathematical epidemiology.

Key words: SIR model, parameter estimation, analytical solution.

Pages of the article in the issue: 40 - 43

Language of the article: Ukrainian

References

AKIN L. & GÖZEL M. G. (2020) Understanding dynamics of pandemics. Turk. J. Med. Sci.. 50. p. 515-519. doi: 10.3906/sag-2004-133

BRATUS, A.S., NOVOZHILOV, A.S. and PLATONOV A.P. (2009) Dinamicheskiye sistemy i modeli biologii. Moskva: Fizmatlit.

KERMACK W.O. & MCKENDRICK A.G. (1927) Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Statistical Society A. 115. p. 700–721. doi: https://doi.org/10.1098/rspa.1927.0118

OLI, M.K., VENKATARAMANA, M., KLEIN, P. A., WENDLAND, L. D. and BROWN, M.B. (2006) Population dynamics of infectious diseases: A discrete time model. Ecological modelling. 198. p. 183–194. doi: https://doi.org/10.1016/j.ecolmodel.2006.04.007

HARKO T., LOBO FRANCISCO S. N. and MAK M. K. (2014) Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates. Applied Mathematics and Computation. 236. p. 184-194.

No 4 (2020)

Downloads

How to Cite

Ivanov, S. M. (2020). Analytical solution and adaptation to the parameter estimation of the SIR model. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (4), 40–43. https://doi.org/10.17721/1812-5409.2020/4.6

Issue

No. 4 (2020)

Section

Computer Science and Informatics

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).