Modeling epidemic in metapopulation networks with heterogeneous diffusion rates

Maoxing Liu; Jie Zhang; Zhengguang Li; Yongzheng Sun; Maoxing Liu; Jie Zhang; Zhengguang Li; Yongzheng Sun

doi:10.3934/mbe.2019355

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7085-7097. doi: 10.3934/mbe.2019355

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Research article

Modeling epidemic in metapopulation networks with heterogeneous diffusion rates

1.
Department of Mathematics, North University of China Taiyuan, Shanxi 030051, P. R. China
2.
School of Science, China University of Mining and Technology Xuzhou, Jiangsu, 221008, P. R. China

Received: 23 March 2019 Accepted: 29 July 2019 Published: 05 August 2019

In this paper, the process of the infectious diseases among cities is studied in metapopulation networks. Based on the heterogeneous diffusion rate, the epidemic model in metapopulation networks is established. The factors affecting diffusion rate are discussed, and the relationship among diffusion rate, connectivity of cities and the heterogeneity parameter of traffic flow is obtained. The existence and stability of the disease-free equilibrium and the endemic equilibrium are analyzed, and epidemic threshold is also obtained. It is shown that the more developed traffic of the city, the greater the diffusion rate, which resulting in the large number of infected individuals; the stronger the heterogeneity of the traffic flow, the greater the threshold of the disease outbreak. Finally, numerical simulations are performed to illustrate the analytical results.
- epidemic,
- metapopulation,
- reaction diffusion process,
- diffusion rate,
- stability
Citation: Maoxing Liu, Jie Zhang, Zhengguang Li, Yongzheng Sun. Modeling epidemic in metapopulation networks with heterogeneous diffusion rates[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7085-7097. doi: 10.3934/mbe.2019355

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Abstract

In this paper, the process of the infectious diseases among cities is studied in metapopulation networks. Based on the heterogeneous diffusion rate, the epidemic model in metapopulation networks is established. The factors affecting diffusion rate are discussed, and the relationship among diffusion rate, connectivity of cities and the heterogeneity parameter of traffic flow is obtained. The existence and stability of the disease-free equilibrium and the endemic equilibrium are analyzed, and epidemic threshold is also obtained. It is shown that the more developed traffic of the city, the greater the diffusion rate, which resulting in the large number of infected individuals; the stronger the heterogeneity of the traffic flow, the greater the threshold of the disease outbreak. Finally, numerical simulations are performed to illustrate the analytical results.

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