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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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    1. Griffeath, David, 1981. "The basic contact processes," Stochastic Processes and their Applications, Elsevier, vol. 11(2), pages 151-185, May.
    2. Ahmed, E. & Agiza, H.N., 1998. "On modeling epidemics Including latency, incubation and variable susceptibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 347-352.
    3. Kuperman, M.N & Wio, H.S, 1999. "Front propagation in epidemiological models with spatial dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 206-222.
    4. Fuentes, M.A. & Kuperman, M.N., 1999. "Cellular automata and epidemiological models with spatial dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 471-486.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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