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Epidemic dynamics: discrete-time and cellular automaton models

Author

Listed:
  • Willox, R.
  • Grammaticos, B.
  • Carstea, A.S.
  • Ramani, A.

Abstract

We present a simple model of population dynamics in the presence of an infection. The model is based on discrete-time equations for sane and infected populations in interaction and correctly describes the dynamics of the epidemic. We find that for some choices of the parameters, the model can possess conserved quantities. We also propose an ultra-discrete, cellular-automaton, version of the model which despite its extremely simple structure still captures the essence of the epidemic dynamics.

Suggested Citation

  • Willox, R. & Grammaticos, B. & Carstea, A.S. & Ramani, A., 2003. "Epidemic dynamics: discrete-time and cellular automaton models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 13-22.
    • Handle: RePEc:eee:phsmap:v:328:y:2003:i:1:p:13-22
    DOI: 10.1016/S0378-4371(03)00552-1
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    Cited by:

    1. Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
    2. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    3. Lee, Sang Dong & Park, Sohyun & Park, Young-Seuk & Chung, Yeong-Jin & Lee, Buom-Young & Chon, Tae-Soo, 2007. "Range expansion of forest pest populations by using the lattice model," Ecological Modelling, Elsevier, vol. 203(1), pages 157-166.
    4. Jalil Rashidinia & Mehri Sajjadian & Jorge Duarte & Cristina Januário & Nuno Martins, 2018. "On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy," Complexity, Hindawi, vol. 2018, pages 1-11, December.
    5. Lu Tang & Yiwang Zhou & Lili Wang & Soumik Purkayastha & Leyao Zhang & Jie He & Fei Wang & Peter X.‐K. Song, 2020. "A Review of Multi‐Compartment Infectious Disease Models," International Statistical Review, International Statistical Institute, vol. 88(2), pages 462-513, August.
    6. Ramani, A. & Carstea, A.S. & Willox, R. & Grammaticos, B., 2004. "Oscillating epidemics: a discrete-time model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 278-292.
    7. Monteiro, L.H.A. & Sasso, J.B. & Chaui Berlinck, J.G., 2007. "Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time," Ecological Modelling, Elsevier, vol. 201(3), pages 553-557.
    8. Shahid, Farah & Zameer, Aneela & Muneeb, Muhammad, 2020. "Predictions for COVID-19 with deep learning models of LSTM, GRU and Bi-LSTM," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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