Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MATHEMATICAL ANALYSIS OF AN "SIR" EPIDEMIC MODEL IN A CONTINUOUS REACTOR - DETERMINISTIC AND PROBABILISTIC APPROACHES

  • Received : 2019.11.24
  • Accepted : 2020.09.21
  • Published : 2021.01.01
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Abstract

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

Keywords

Acknowledgement

The authors thank the anonymous referees for their constructive comments and helpful suggestions that improved the presentation of this paper.

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