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Oscillating epidemics: a discrete-time model

Author

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

Abstract

We study a model of an epidemic where the individuals which are cured from the infection are not permanently immunised but have a finite probability of becoming reinfected. We show that the epidemic does not follow the usual pattern of growth and decay but rather oscillates towards an “endemic” fixed point, where a certain number of infectives may persist. We present a discrete-time version of the model which may also serve as an integrator of the continuous-time one. An appropriate choice of the discrete system allows the derivation of a cellular-automaton version, which incorporates the essential dynamical behaviour of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:333:y:2004:i:c:p:278-292
    DOI: 10.1016/j.physa.2003.10.051
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    References listed on IDEAS

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    1. 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.
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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. Yuanyuan Ma & Lingxuan Li, 2018. "Crisis Spreading Model of the Shareholding Networks of Listed Companies and Their Main Holders and Their Controllability," Complexity, Hindawi, vol. 2018, pages 1-17, December.
    3. 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.
    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.

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