The impact of media on the spatiotemporal pattern dynamics of a reaction-diffusion epidemic model

Xin-You Meng; Tao Zhang; Xin-You Meng; Tao Zhang

doi:10.3934/mbe.2020223

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4034-4047. doi: 10.3934/mbe.2020223

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The impact of media on the spatiotemporal pattern dynamics of a reaction-diffusion epidemic model

Xin-You Meng ^,,
Tao Zhang

School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received: 03 March 2020 Accepted: 27 May 2020 Published: 03 June 2020

In this paper, a reaction-diffusion SI epidemic model with media impact is considered. The boundedness of system and the existence of the state are given. The local stabilities of the endemic states are analyzed. Sufficient conditions of the occurrence of the Turing pattern are obtained by the center manifold theorem and normal form method. Some numerical simulations are given to check in the theoretical results. We find that the influence of media not only inhibits the spread of infectious diseases, but also effects the spatial steady-state of model.
- epidemic model,
- media impact,
- spatiotemporal distribution,
- Turing instability
Citation: Xin-You Meng, Tao Zhang. The impact of media on the spatiotemporal pattern dynamics of a reaction-diffusion epidemic model[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4034-4047. doi: 10.3934/mbe.2020223

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Abstract

In this paper, a reaction-diffusion SI epidemic model with media impact is considered. The boundedness of system and the existence of the state are given. The local stabilities of the endemic states are analyzed. Sufficient conditions of the occurrence of the Turing pattern are obtained by the center manifold theorem and normal form method. Some numerical simulations are given to check in the theoretical results. We find that the influence of media not only inhibits the spread of infectious diseases, but also effects the spatial steady-state of model.

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