### Mathematical Biosciences and Engineering

2020, Issue 4: 3062-3087. doi: 10.3934/mbe.2020174
Research article Special Issues

# Spread trend of COVID-19 epidemic outbreak in China: using exponential attractor method in a spatial heterogeneous SEIQR model

• Received: 09 March 2020 Accepted: 08 April 2020 Published: 13 April 2020
• In this paper we introduce a method of global exponential attractor in the reaction-diffusion epidemic model in spatial heterogeneous environment to study the spread trend and long-term dynamic behavior of the COVID-19 epidemic. First, we prove the existence of the global exponential attractor of general dissipative evolution systems. Then, by using the existence theorem, the global asymptotic stability and the persistence of epidemic are discussed. Finally, combine with the official data of the COVID-19 and the national control strategy, some numerical simulations on the stability and global exponential attractiveness of the COVID-19 epidemic are given. Simulations show that the spread trend of the epidemic is in line with our theoretical results, and the preventive measures taken by the Chinese government are effective.

Citation: Cheng-Cheng Zhu, Jiang Zhu. Spread trend of COVID-19 epidemic outbreak in China: using exponential attractor method in a spatial heterogeneous SEIQR model[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3062-3087. doi: 10.3934/mbe.2020174

### Related Papers:

• In this paper we introduce a method of global exponential attractor in the reaction-diffusion epidemic model in spatial heterogeneous environment to study the spread trend and long-term dynamic behavior of the COVID-19 epidemic. First, we prove the existence of the global exponential attractor of general dissipative evolution systems. Then, by using the existence theorem, the global asymptotic stability and the persistence of epidemic are discussed. Finally, combine with the official data of the COVID-19 and the national control strategy, some numerical simulations on the stability and global exponential attractiveness of the COVID-19 epidemic are given. Simulations show that the spread trend of the epidemic is in line with our theoretical results, and the preventive measures taken by the Chinese government are effective.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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