Research article Special Issues

Influence of spatial heterogeneous environment on long-term dynamics of a reaction-diffusion SVIR epidemic model with relaps

  • Received: 27 February 2019 Accepted: 27 May 2019 Published: 24 June 2019
  • In this paper by adding the factors of disease relapse and vaccination in the space hetero-geneous environment, we establish and discuss a class of reaction-diffusion SVIR model with relapse and a varying external source in spatial heterogeneous environment. By applying a different method than the Lyapunov function, we study the long-term dynamic behavior of this model by means of global exponential attractor theory and gradient flow method. The global asymptotic stability and the persistence of epidemic are proved. To test the validity of our theoretical results, we choose some specific epidemic disease with some more practical and more definitive official data to simulate the global stability and exponential attraction of the model. The simulation results showed that the factors of disease relapse, vaccination and spatial heterogeneity had a great influence on the persists uniformly of the disease.

    Citation: Cheng-Cheng Zhu, Jiang Zhu, Xiao-Lan Liu. Influence of spatial heterogeneous environment on long-term dynamics of a reaction-diffusion SVIR epidemic model with relaps[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5897-5922. doi: 10.3934/mbe.2019295

    Related Papers:

  • In this paper by adding the factors of disease relapse and vaccination in the space hetero-geneous environment, we establish and discuss a class of reaction-diffusion SVIR model with relapse and a varying external source in spatial heterogeneous environment. By applying a different method than the Lyapunov function, we study the long-term dynamic behavior of this model by means of global exponential attractor theory and gradient flow method. The global asymptotic stability and the persistence of epidemic are proved. To test the validity of our theoretical results, we choose some specific epidemic disease with some more practical and more definitive official data to simulate the global stability and exponential attraction of the model. The simulation results showed that the factors of disease relapse, vaccination and spatial heterogeneity had a great influence on the persists uniformly of the disease.
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    © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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