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Stationary states and spatial patterning in an SIS epidemiology model with implicit mobility

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  • Ilnytskyi, Jaroslav
  • Kozitsky, Yuri
  • Ilnytskyi, Hryhoriy
  • Haiduchok, Olena

Abstract

By means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an SIS model, in which the individuals are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size q. Here we consider the following cases: q is fixed at certain value; and q is taken at random at each step and for each individual. The obtained numerical data are then mapped onto the solution of its version, corresponding to the limit q→∞. This allows for deducing an explicit form of the dependence of the fraction of infected individuals on the curing rate γ. A detailed analysis of the appearance of spatial patterns of infected individuals in the stationary state is performed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:36-45
    DOI: 10.1016/j.physa.2016.05.006
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Ramos, A.B.M. & Schimit, P.H.T., 2019. "Disease spreading on populations structured by groups," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 265-273.
    3. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.

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