Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (6): 861-875.doi: 10.3969/j.issn.1005-3085.2015.06.007

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Analysis of Animal Disease Transmission Model with Migration of Nearby Meadows

FAN Jie-ru1,   JIN Zhen1,2   

  1. 1- Department of Mathematics, Faculty of Science, North University of China, Taiyuan, Shanxi 030051
    2- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006
  • Received:2014-03-28 Accepted:2015-01-12 Online:2015-12-15 Published:2016-02-15
  • Supported by:
    The National Natural Science Foundation of China (11171314; 11331009).

Abstract:

The paper mainly examines the influemce of cross-infection among meadows and animal migration on the spread of animal diseases. Firstly, based on mechanism of epidemic transition, an animal disease spreading model with animal migration among adjacent meadows is established. Then, applying the qualitative stability theory of differential equations, we discuss the existence of disease-free equilibrium and endemic equilibrium, proving that the disease-free equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to verify the theoretical analysis results and the sensitivity of the basic reproduction number with respect to different parameters. The results indicate that the transmission coefficient of individuals contacting the bacteria around environment and the coefficient of individuals immigration from nonadjacent farms have signifiant influence on the basic reproduction number.

Key words: migration, basic reproduction number, stability, continuity

CLC Number: