标题： 非稳态尾部在动力学流行病模型中的控制 显示英文标题

标题： Control of Overpopulated Tails in Kinetic Epidemic Models

摘要： 我们为数学流行病学中的受控分 compartmental 模型引入基于模型的转移率，重点研究控制策略对描述接触形成动力学的相互作用多智能体系统的影响。 在动能控制问题的框架下，我们比较两种典型的控制协议：一种是直接影响动力学的加性控制，另一种是针对智能体之间相互作用强度的控制。 对于 SIR 分 compartmental 化，推导出出现的受控宏观模型，以说明其对流行病进展和接触相互作用动力学的影响。 数值结果表明，这种方法在引导动力学和控制流行病趋势方面的有效性，即使在接触分布表现出过度填充尾部的情况下也是如此。 显示英文摘要

摘要： We introduce model-based transition rates for controlled compartmental models in mathematical epidemiology, with a focus on the effects of control strategies applied to interacting multi-agent systems describing contact formation dynamics. In the framework of kinetic control problems, we compare two prototypical control protocols: one additive control directly influencing the dynamics and another targeting the interaction strength between agents. The emerging controlled macroscopic models are derived for an SIR compartmentalization to illustrate their impact on epidemic progression and contact interaction dynamics. Numerical results show the effectiveness of this approach in steering the dynamics and controlling epidemic trends, even in scenarios where contact distributions exhibit an overpopulated tail.