Modeling and analysis of the transmission dynamics of cystic echinococcosis: Effects of increasing the number of sheep

Yiwei He; Qianqian Cui; Zengyun Hu; Yiwei He; Qianqian Cui; Zengyun Hu

doi:10.3934/mbe.2023653

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14596-14615. doi: 10.3934/mbe.2023653

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Research article

Modeling and analysis of the transmission dynamics of cystic echinococcosis: Effects of increasing the number of sheep

Yiwei He ¹,
Qianqian Cui ^{1
,
,},
Zengyun Hu ^{2
,
,}

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2.
State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China

Academic Editor: Jia Li

Received: 09 May 2023 Revised: 06 June 2023 Accepted: 13 June 2023 Published: 05 July 2023

A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.
- epidemic model,
- cystic echinococcosis,
- basic reproduction number,
- global asymptotic stability,
- sensitivity analysis
Citation: Yiwei He, Qianqian Cui, Zengyun Hu. Modeling and analysis of the transmission dynamics of cystic echinococcosis: Effects of increasing the number of sheep[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14596-14615. doi: 10.3934/mbe.2023653

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Abstract

A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.

References

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