Global dynamics and optimal control strategies for the brucellosis model with environmental saturation infection: An assessment of severely affected provinces in China

In this paper, we develop a multidimensional dynamic model involving the sheep population, the human population, and the brucella in the environment to explore the potential impact of key factors on brucellosis in six high-prevalence provinces in China. The transmission of environment-to-individual in this model is described in the form of saturated infections. We first determine the basic reproduction number R0 and analyze the global asymptotic stability of the disease-free and endemic equilibriums by introducing the Volterra–Lyapunov stability matrix theory into the classical Lyapunov function method. Secondly, by using actual human brucellosis data from these provinces over the past 18 years to estimate the parameter values in the model, we have determined that the current basic reproduction numbers of brucellosis in these regions are greater than 1. This implies that brucellosis will persist in these provinces under the current control efforts. Our simulation results indicate that the most effective strategy for reducing the disease burden in these provinces is to simultaneously increase the intensity of vaccination efforts and strengthen the culling of infected sheep. Utilizing Pontryagin’s maximum principle, we derive temporal outcomes for the implementation of a strategy aimed at achieving minimal costs. Furthermore, we find that, under lower cost constraints, the culling measures can be executed at maximum intensity for an extended duration while maintaining the existing vaccination schedule. These findings can provide important insights for relevant prevention and control efforts.