论文标题
具有标签开关的多代理系统的Boltzmann型方程
Boltzmann-type equations for multi-agent systems with label switching
论文作者
论文摘要
在本文中，我们提出了质量变体相互作用多代理系统的玻尔兹曼型动力学描述。我们的代理人的特征是微观状态，由于它们的相互作用而变化，并通过标签，它标识了它们所属的群体。除了在各组内部和跨组之间进行交互之外，代理还可以根据州依赖的马尔可夫型跳跃过程更改标签。我们得出了每组关节相互作用/标签开关过程的一般动力学方程。对于原型出生/死亡动力学，我们通过Fokker-Planck渐近分析表征了组的瞬时和平衡动力学分布。然后，我们介绍并分析了一个简单的传染病模型，该模型利用了关节相互作用/标签开关过程来描述隔离措施。
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.
