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Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model

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  • Ilnytskyi, Jaroslav
  • Pikuta, Piotr
  • Ilnytskyi, Hryhoriy

Abstract

We report computer simulation studies of the SEIS cellular automaton epidemiology model which takes into account explicitly the incubation period of the infection by considering separate fractions for the exposed E and infectious I individuals. The model is considered on a square lattice and the analysis is performed in various regimes covering cases of short and long incubation period at a range of contact rates. We found the critical curing rate to be independent on the incubation period, reflecting similarity between the SEIS model and the SI′S one, where I′=E+S. The stationary state of the lattice-based SEIS model compared to that of its compartment analogue indicates essential deviation between both at low contact rates. At long incubation period and high contact rates, the ratio between the values of E and I in a stationary state is found to depend strongly on the curing rate emphasizing the huge role of curing efficiency in this case. It was found that, upon approaching the critical curing rate, the time needed to reach a stationary state diverges, the effect reminiscent of critical slowing down. Visualization of the initial stage of the infection spread reveals porous clusters of infectious individuals with their surface decorated by exposed individuals.

Suggested Citation

  • Ilnytskyi, Jaroslav & Pikuta, Piotr & Ilnytskyi, Hryhoriy, 2018. "Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 241-255.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:241-255
    DOI: 10.1016/j.physa.2018.06.001
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    References listed on IDEAS

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    1. Ilnytskyi, Jaroslav & Kozitsky, Yuri & Ilnytskyi, Hryhoriy & Haiduchok, Olena, 2016. "Stationary states and spatial patterning in an SIS epidemiology model with implicit mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 36-45.
    2. J. Asikainen & A. Aharony & B. Mandelbrot & E. Rausch & J.-P. Hovi, 2003. "Fractal geometry of critical Potts clusters," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(4), pages 479-487, August.
    3. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    4. van Wijland, F. & Oerding, K. & Hilhorst, H.J., 1998. "Wilson renormalization of a reaction–diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(1), pages 179-201.
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    1. Tomovski, Igor & Basnarkov, Lasko & Abazi, Alajdin, 2022. "Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).

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    Keywords

    Epidemiology; Cellular automata;

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