WSEAS Transactions on Biology and Biomedicine


Print ISSN: 1109-9518
E-ISSN: 2224-2902

Volume 15, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Mathematical Models of Epidemics in Closed Populations and their Visualization via Web Application PhaPl

AUTHORS: Irina Astashova, Victoria Chebotaeva, Aleksey Cherepanov

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ABSTRACT: Mathematical modeling of the spread of epidemics is one of the main problems in mathematical biology. In this paper, we will consider dynamical systems describing epidemics models, examine the stability of solution to the system in the neighborhood of equilibrium points, and construct phase portraits for its special cases with the help of PhaPl web application.

KEYWORDS: Mathematical modeling in biology, epidemics, nonlinear dynamical system, phase portrait, web application

REFERENCES:

[1] H.W. Hethcote and P. van den Driessche, Some epidemiological models with nonlinear incidence, Journal of Mathematical Biology, 1991.

[2] PhaPl: Phase Plane Helper, URL: https://phapl.github.io/phapl.en.html , (2018).

[3] Cherepanov A., PhaPl: software to plot and research phase portraits automatically, Otkrytoe obrazovanie, Vol.21, No.3, 2017, pp. 66–72. (Russian)

[4] Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and Cert ˇ ´ık, Ondˇrej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, et al., SymPy: symbolic computing in Python, PeerJ Computer Science, Vol.3, 2017, e103, https://doi.org/10.7717/peerj-cs.103

[5] Diekmann O. and Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, John Wiley and Sons, 2000.

[6] A.Bratus, A.Novozhilov, A.Platonov, Dynamic systems and models in biology, Draft, published in Russian, 2011.

WSEAS Transactions on Biology and Biomedicine, ISSN / E-ISSN: 1109-9518 / 2224-2902, Volume 15, 2018, Art. #12, pp. 112-118


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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