Background Brucellosis is a chronic zoonotic disease, and Ningxia is one of the high prevalence regions in China. To mitigate the spread of brucellosis, the government of Ningxia has implemented a comprehensive prevention and control plan (2022-2024). It is meaningful to quantitatively evaluate the accessibility of this strategy. Methods Based on the transmission characteristics of brucellosis in Ningxia, we propose a dynamical model of sheep-human-environment, which coupling with the stage structure of sheep and indirect environmental transmission. We first calculate the basic reproduction number $$R_0$$ R 0 and use the model to fit the data of human brucellosis. Then, three widely applied control strategies of brucellosis in Ningxia, that is, slaughtering of sicked sheep, health education to high risk practitioners, and immunization of adult sheep, are evaluated. Results The basic reproduction number is calculated as $$R_{0}=1.47$$ R 0 = 1.47 , indicating that human brucellosis will persist. The model has a good alignment with the human brucellosis data. The quantitative accessibility evaluation results show that current brucellosis control strategy may not reach the goal on time. “Ningxia Brucellosis Prevention and Control Special Three-Year Action Implementation Plan (2022-2024)” will be achieved in 2024 when increasing slaughtering rate $$\gamma$$ γ by 30$$\%$$ % , increasing health education to reduce $$\beta _{h}$$ β h to 50$$\%$$ % , and an increase of immunization rate of adult sheep $$\theta$$ θ by 40$$\%$$ % . Conclusion The results demonstrate that the comprehensive control measures are the most effective for brucellosis control, and it is necessary to further strengthen the multi-sectoral joint mechanism and adopt integrated measures to prevention and control brucellosis. These results can provide a reliable quantitative basis for further optimizing the prevention and control strategy of brucellosis in Ningxia.
The long-term statistical rule is one of the important questions for stochastic pollution-population dynamical models, thus it would be worth looking for the stationary distribution as an indicator in analysing the effects of toxicant and noises on the variation of population in evolution process. In present paper, we investigate a stochastic single-species model under regime switching in a polluted environment. By use of the ergodic of Markov chain and constructing Lyapunov function, the sufficient conditions for the positive recurrence and ergodic property are established, which imply the existence of stationary distribution of the model. Moreover, the mean and variance of marginal stationary distribution are estimated. Our analysis indicates that the coloured noise and toxicant may play an important role in determining the shape of stationary distribution and its statistics characteristics. Finally, numerical simulations are carried out to support our theoretical results.
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