Modeling of clustering and spread of diseases with multidrug pathogens

Authors

  • Г.І. Ільницький
  • Я.М. Ільницький

DOI:

https://doi.org/10.18372/2310-5461.28.9671

Keywords:

epidemiology model, multi drug resistant carrier, cellular automata

Abstract

The epidemiology model for the non-immune disease with both ordinary and multi drug resistant carriers tuberculosis is considered via cellular automata algorithm on a square lattice. The early stage and stationary state of the disease are studied in various epidemiology regimes, as well as relative prevalence of multi drug resistant carrier, spatial patterns and clusterisation of infected individuals.

References

Kermack W. O., McKendrick A. G., A contribu-tion to the mathematical theory of epidemics // Pro-ceedings of Royal Society London. A, 115 (1927). — P. 700–721.

Brauer F., The Kermack–McKendrick epidemic model revisited // Mathematical Biosciences, 198 (2005). — P. 119–131.

Sun R. Global stability of the endemic equilibri-um of multigroup SIR models wih nonlinear incidence // Computers and Mathematics with Applications 60 (2010). — P. 2286–2291.

Hu Z., Tenga Zh., Jiang H. Stability analysis in a class of discrete SIRS epidemic models // Nonlinear Analysis: Real World Applications 13 (2012). — P. 2017–2033.

Boccara N. Automata network models of inter-acting populations, in Cellular Automata, Dynamical Systems and Neural Networks, Mathematics and Its Applications series, E. Goles and S. Martines, Eds. Vol. 282, Springer, 1994. — 192 p.

Situngkir H. Epidemiology Through Cellular Automata: Case of Study Avian Influenza in Indonesia, 2004, arXiv:nlin/0403035.

Albert R. Barabasi A.-L. Statistical mechanics of complex networks. Reviews of Modern Physics 74 (2002) . — P. 47–97.

Sabag M.M.S., de Oliveira M.J. Conserved con-tact process in one to five dimensions // Physical Re-view E 66 (2002), 036115.

Ilnytskyi J., Holovatch Y., Kozitsky Y., Ilnytskyi H. Computer simulations of a stochastic model for the non-immune disease spread. — Вісник НУ «Львівсь-ка Політехніка» No. 800 (2014). — С. 176–185.

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Published

2015-11-09

How to Cite

Ільницький, Г., & Ільницький, Я. (2015). Modeling of clustering and spread of diseases with multidrug pathogens. Science-Based Technologies, 28(4), 296–300. https://doi.org/10.18372/2310-5461.28.9671

Issue

Vol. 28 No. 4 (2015)

Section

Information and Communication Systems and Networks

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