Dynamic analysis of sheep Brucellosis model with environmental infection pathways

Zongmin Yue; Yuanhua Mu; Kekui Yu; Zongmin Yue; Yuanhua Mu; Kekui Yu

doi:10.3934/mbe.2023520

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11688-11712. doi: 10.3934/mbe.2023520

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Dynamic analysis of sheep Brucellosis model with environmental infection pathways

1.
Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China
2.
Yulin Science and Technology Bureau, Yulin 719053, China

Academic Editor: Xiang-Sheng Wang

Received: 16 March 2023 Revised: 26 April 2023 Accepted: 27 April 2023 Published: 08 May 2023

We develop a mathematical model for the transmission of brucellosis in sheep taking into account external inputs, immunity, stage structure and other factors. We find the the basic reproduction number $ R_0 $ in terms of the model parameters, and prove the global stability of the disease-free equilibrium. Then, the existence and global stability of the endemic equilibrium is proven. Finally, sheep data from Yulin, China are employed to fit the model parameters for three different environmental infection exposure conditions. The variability between different models in terms of control measures are analyzed numerically. Results show that the model is sensitive to the control parameters for different environmental infection exposure functions. This means that in practical modeling, the selection of environmental infection exposure functions needs to be properly considered.
- Brucellosis,
- multi-structure,
- environmental infection function,
- control parameter
Citation: Zongmin Yue, Yuanhua Mu, Kekui Yu. Dynamic analysis of sheep Brucellosis model with environmental infection pathways[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11688-11712. doi: 10.3934/mbe.2023520

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Abstract

We develop a mathematical model for the transmission of brucellosis in sheep taking into account external inputs, immunity, stage structure and other factors. We find the the basic reproduction number $ R_0 $ in terms of the model parameters, and prove the global stability of the disease-free equilibrium. Then, the existence and global stability of the endemic equilibrium is proven. Finally, sheep data from Yulin, China are employed to fit the model parameters for three different environmental infection exposure conditions. The variability between different models in terms of control measures are analyzed numerically. Results show that the model is sensitive to the control parameters for different environmental infection exposure functions. This means that in practical modeling, the selection of environmental infection exposure functions needs to be properly considered.

References

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