A two-stage control strategy for sheep brucellosis with discontinuous changes in vaccination rate
摘要
Vaccination serves as a pivotal measure for controlling brucellosis in sheep flocks, and the optimization of vaccination strategies has a decisive impact on infectious disease containment outcomes. Existing studies primarily employ constant or continuously time-varying vaccination strategies based on optimal control theory, typically applied to routine vaccination scenarios. This paper refers to such approaches as single-stage control. However, such strategies failed to accurately address the urgent need to significantly increase vaccination rates during the sudden outbreak of the infectious disease. To describe this situation, this study proposes a two-stage control strategy designed to more effectively respond to sudden outbreaks through discontinuous vaccination rates. We first constructed a single-stage SEIBV optimal control model incorporating time-varying birth rates and introducing reproductive losses, with reproductive losses included in the cost function. Secondly, within this framework, we rigorously proved the existence and uniqueness of the single-stage optimal control solution. Based on this, we designed a two-stage intervention strategy and theoretically analyzed and explicitly established the sufficient conditions under which this strategy outperforms a single-stage strategy in terms of cumulative cases. We also determined the corresponding timing for boosting vaccination rates. Finally, numerical simulations validated the reliability of the theoretical analysis, confirming that the two-stage control strategy effectively reduces both cumulative cases and cumulative comprehensive losses. This study provides new theoretical insights and practical pathways for the cost-effective prevention and control of brucellosis.