Dynamical analysis and optimal control strategy of seasonal brucellosis

Abstract

Brucellosis exhibits typical seasonal patterns and shows a notable rising trend in recent years, posing a serious threat to public health and economic development. Experimental research indicates that increased tick activity may elevate brucellosis transmission risk although the quantitative impact of ticks remains insufficiently explored. To investigate the seasonal transmission mechanisms of Brucella, identify the key factors, and assess ticks’ potential role, a multi-population non-autonomous periodic dynamical model is developed. The global dynamics of the model such as extinction, uniform persistence, disease-free periodic solution, and endemic periodic solution are well explored in terms of the basic reproduction number. Theoretical and numerical analyses demonstrate that, while tick control helps mitigate transmission risks, it is insufficient to eliminate periodic transmission. Effective control of brucellosis requires a comprehensive approach, especially culling infected sheep and improving vaccination coverage to curb the overall rising trend. Additionally, adjusting sheep reproductive schedules within the sheep’s life cycle, such as delaying the peak time of birth and advancing the peak time of abortion, is crucial for managing seasonal transmission. Numerical simulations of the optimal control strategies reveal that adjusting interventions based on seasonal fluctuations in infections balances the cost and effectiveness while highlighting the importance of effective tick control.