疫情沿交通工具跨区域扩散建模及最优控制

交通运输系统在服务民众的同时也为疫情沿跨区域传播扩散提供了载体.鉴于此,研究疫情沿多种交通工具跨区域扩散模型及最优控制问题.考虑人口空间状态、迁徙过程、疫情状态和交通工具特征,构建多区域迁徙-疫情扩散耦合动力学方程,并分析其扩散性质.综合考虑应急资源的有限性,进一步建立基于本地与迁徙隔离政策的动态最优控制模型.数值计算对比分析不同管控策略组合下疫情的扩散速度与范围,验证疫情扩散模型和最优控制策略的有效性.结果表明:疫情可以借助交通工具快速扩散;仅对单一交通工具实施管控措施可以快速降低疫情跨区域扩散的速度,但对均衡状态的扩散范围影响小.

Multi-regional epidemic spreading in transportation network: Modelling and optimal control strategies

Transportation systems facilitate the spread of pandemics across regions. This paper studies the modeling and optimal control of epidemic spreading with inter-city travel by train and bus. Considering the population spatial status, migration process, epidemic status and transport modes, a multi-regional migration-epidemic diffusion model is established by using dynamic equations, and the diffusion properties are analyzed. With the limited emergency resources, a dynamic optimal control model considering local and migration isolation strategies is also developed. Numerical examples are given to compare the spread speed and scope of the epidemic under different control strategies, which verify the effectiveness of the proposed optimal control strategies. The results demonstrate that the epidemic can spread rapidly via the transportation system. Implementing a control strategy for the certain type of transportation modes can quickly reduce the speed of cross-regional diffusion, but has little impact on the diffusion scope of the equilibrium state.