Transmission dynamics and optimal control of brucellosis in Inner Mongolia of China

Linhua Zhou; Meng Fan; Qiang Hou; Zhen Jin; Xiangdong Sun; Linhua Zhou; Meng Fan; Qiang Hou; Zhen Jin; Xiangdong Sun

doi:10.3934/mbe.2018025

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 2: 543-567. doi: 10.3934/mbe.2018025

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Transmission dynamics and optimal control of brucellosis in Inner Mongolia of China

1.
Department of Applied Mathematics, School of Science, Changchun University of Science and Technology, Changchun 130022, China
2.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3.
School of Mechatronic Engineering, North University of China, Taiyuan 030051, China
4.
Complex Systems Research Center, Shanxi University Taiyuan 030006, China
5.
China Animal Health And Epidemiology Center, Qingdao 266032, China

Received: 28 November 2016 Accepted: 15 March 2017 Published: 01 April 2018
MSC : Primary: 92D30, 34D23; Secondary: 49J15

A multigroup model is developed to characterize brucellosis transmission, to explore potential effects of key factors, and to prioritize control measures. The global threshold dynamics are completely characterized by theory of asymptotic autonomous systems and Lyapunov direct method. We then formulate a multi-objective optimization problem and, by the weighted sum method, transform it into a scalar optimization problem on minimizing the total cost for control. The existence of optimal control and its characterization are well established by Pontryagin's Maximum Principle. We further parameterize the model and compute optimal control strategy for Inner Mongolia in China. In particular, we expound the effects of sheep recruitment, vaccination of sheep, culling of infected sheep, and health education of human on the dynamics and control of brucellosis. This study indicates that current control measures in Inner Mongolia are not working well and Brucellosis will continue to increase. The main finding here supports opposing unregulated sheep breeding and suggests vaccination and health education as the preferred necessary emergency intervention control. The policymakers must take a new look at the current control strategy, and, in order to control brucellosis better in Inner Mongolia, the governments have to preemptively press ahead with more effective measures.
- Brucellosis,
- epidemic model,
- dynamical analysis,
- global stability,
- optimal control
Citation: Linhua Zhou, Meng Fan, Qiang Hou, Zhen Jin, Xiangdong Sun. Transmission dynamics and optimal control of brucellosis in Inner Mongolia of China[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 543-567. doi: 10.3934/mbe.2018025

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Abstract

A multigroup model is developed to characterize brucellosis transmission, to explore potential effects of key factors, and to prioritize control measures. The global threshold dynamics are completely characterized by theory of asymptotic autonomous systems and Lyapunov direct method. We then formulate a multi-objective optimization problem and, by the weighted sum method, transform it into a scalar optimization problem on minimizing the total cost for control. The existence of optimal control and its characterization are well established by Pontryagin's Maximum Principle. We further parameterize the model and compute optimal control strategy for Inner Mongolia in China. In particular, we expound the effects of sheep recruitment, vaccination of sheep, culling of infected sheep, and health education of human on the dynamics and control of brucellosis. This study indicates that current control measures in Inner Mongolia are not working well and Brucellosis will continue to increase. The main finding here supports opposing unregulated sheep breeding and suggests vaccination and health education as the preferred necessary emergency intervention control. The policymakers must take a new look at the current control strategy, and, in order to control brucellosis better in Inner Mongolia, the governments have to preemptively press ahead with more effective measures.

References

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