GLOBAL DYNAMICS OF A GENERAL BRUCELLOSIS MODEL WITH DISCRETE DELAY

Qiang Hou; Feng Zhang

doi:10.11948/2016019

2016 Volume 6 Issue 1

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Qiang Hou, Feng Zhang. GLOBAL DYNAMICS OF A GENERAL BRUCELLOSIS MODEL WITH DISCRETE DELAY[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 227-241. doi: 10.11948/2016019

Citation:

Qiang Hou, Feng Zhang. GLOBAL DYNAMICS OF A GENERAL BRUCELLOSIS MODEL WITH DISCRETE DELAY[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 227-241. doi: 10.11948/2016019

GLOBAL DYNAMICS OF A GENERAL BRUCELLOSIS MODEL WITH DISCRETE DELAY

Qiang Hou^1,2,
Feng Zhang¹

1 School of Mathematics and Statistics, Southwest University, No.2 Tiansheng Road, Chongqing 400715, China;
2 Department of Mathematics, North University of China, No.3 Xueyuan Road, Taiyuan 030051, Shanxi Province, China

Fund Project:

Abstract

Abstract

For the prevention and control of brucellosis, it is important to investigate the mechanism of brucellosis transmission. Based on the characteristics of the spread of brucellosis, a susceptible-exposed-infectious-brucella (SEIB) delay dynamic model is proposed with the general incidence, elimination rate and shedding rate of pathogen. Under biologically motivated assumptions, it shows the uniqueness of the endemic equilibrium, and investigates the global asymptotically stability of the disease-free equilibrium and the endemic equilibrium. The results suggest that the global stability of equilibria depends entirely on the basic reproduction number R₀ and time delay is harmless for the stability of equilibria. Finally, some specific examples and numerical simulations are used to illustrate the utilization of research results and reveal the biological significance of hypothesis (H₇), which implies that the dynamics of brucellosis transmission depend largely on the development of the prevention and control strategies.
- Brucellosis /
- indirect transmission /
- discrete delay /
- global stability /
- Lyapunov function
MSC: 34D20;37N25

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References

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