Abstract: In recent years, a series of pandemics, including Mpox and Avian influenza, have not only severely impacted public health but also resulted in substantial economic losses worldwide. Consequently, governments across the globe are confronted with the critical challenge of effectively managing potential public health emergencies. In the practices of pandemic prevention, it is evident that the timely implementation of appropriate intervention measures is crucial for controlling the spread of such emergencies. Therefore, it is imperative for governments to develop an effective dynamic intervention scheme for modulating population mobility. Despite its importance, there is scarce research exploring this critical scheme. To account for the dynamic of government intervention measures,public mobility,and the characteristics of pandemics, this paper develops a differential game framework including the government and the public.
To capture the changing trends of the pandemic, we incorporate the Susceptible-Infective-Susceptible (SIS) epidemic model into the framework. We analyze the optimal levels of government intervention measures intensity and public mobility under both baseline and pandemic containment scenarios and then research the timing of implementing intervention measures from the perspectives of the cost of pandemic prevention and public behavior. We then discuss the correlation between the intensity of government intervention measures and the level of public mobility. Furthermore, we conduct an extensive numerical analysis to thoroughly examine the findings derived from our theoretical model. We collect the experimental data from the documents of authoritative organizations like WHO and the literature on epidemic containment to conduct numerical experiments. In extended model, we discuss the interaction between the intensity of government intervention measures and the level of public mobility in a societal epidemic prevention and control system.
Our findings show that the government should implement intervention measures as soon as possible from the perspective of the cost of pandemic prevention. Specifically, the correlation between the pandemic trends and the cost of pandemic prevention is not a linear relationship. Increasing the intensity of intervention measures incurs a higher cost. From the perspective of public behavior, facing a major public health emergency with high transmission rates, governments must implement intervention measures to control the pandemic. Facing general public health emergencies with low transmission rates, the government should not implement intervention measures too early to avoid social panic. As a result, the government should comprehensively determine the timing of implementing intervention measures, taking into account the cost of prevention and public behavior. Second, intense intervention measures are not always better. The results indicate that the appropriate relationship between the level of public activity and the intensity of government intervention is influenced by various factors. Consequently, the government should focus on the coordination between intervention strategies and public behavioral responses and further adjust the intensity of intervention measures within an appropriate range based on the needs and risks of the public, to avoid causing more serious social problems. Finally, a higher risk of infection does not necessarily deter the public from engaging in outdoor activities. Infected individuals may still require outdoor medical visits. As the epidemic situation deteriorates and public mobility increases, the government must escalate intervention measures in response to heightened infection risks.
Although this paper provides several important findings and management implications, there are still some limitations. First, future research can discuss the impact of virus mutation. Second, the infected public has different clinical manifestations. In the future, the multi-compartment epidemic model should be used to classify the public and design intervention measures for different public groups. Finally, the government can also take drug interventions. Hence, further research could study how to optimize the combination of government intervention measures.

Key words: public health emergencies, public behavior, intervention measure timing, differential game

摘要： 如何应对未来的突发公共卫生事件是世界各国政府面临的重要问题。在恰当的时机,实施合理的干预措施是控制突发公共卫生事件扩散蔓延的关键。为此,政府需要设计有效的公众外出行为动态干预机制。本文通过Susceptible-Infective-Susceptible(SIS)传染病模型刻画政府干预措施、公众外出行为、传染病变化趋势之间的动态关系,构建包含政府和公众的微分博弈模型,得到基础情景和防控情景下政府最优干预措施力度和公众最优外出活动水平,分别从防疫成本和公众行为视角分析政府实施干预措施的时机,讨论政府干预措施力度与公众外出活动水平之间的协调关系。研究发现,基于防疫成本视角,政府应尽早实施干预措施。从公众行为视角来看,面对传染率较高的重大公共卫生突发事件时,政府才需要立即采取干预措施。其次,政府的干预措施力度并非越大越好,注重与公众行为之间的协调关系才能实现精准防控。最后,较高的感染风险不一定降低公众的外出活动水平。

关键词: 突发公共卫生事件, 公众行为, 干预措施实施时机, 微分博弈