In recent years, frequent public health emergencies have caused enormous harm to economic development and the safety of human life. The year 2022 saw a rebound of the global epidemic under the influence of the new virus strain “Omicron”, with newly confirmed cases in the Chinese mainland exceeding 1000 for several consecutive days. To reduce the damage caused by major public health emergencies, it is necessary to reserve and provide a large number of emergency supplies for the affected area. Due to the uncertainty in the probability and demand of public health emergencies, which can easily lead to a shortage of supplies and untimely treatment, the importance of joint reserve work for emergency medical supplies is highlighted. The report to the 20th National Congress of the Communist Party of China pointed out that it is necessary to enhance the capacity of disaster prevention, mitigation, and relief and the handling of major public emergencies, and strengthen the construction of national and regional emergency forces. Meanwhile, the “14th Five-Year Plan” on the national emergency system proposed to select qualified enterprises to be included in enterprises for capacity reserve and establish a dynamic update and adjustment mechanism. Therefore, how to implement the joint reserve work of the government and enterprises for emergency medical supplies in the events of public health emergencies and improve the efficiency of the emergency supply chain has become a hot topic of concern for current scholars.Existing research on the reserve of emergency medical supplies has rarely explored the joint reserve model of the government and enterprises and considered the delayed effects and research on disappointment aversion is still mainly limited to static mathematical function solving in the commercial field. In addition, existing literature rarely takes the storage cycle and value decay of medical supplies into account, and a small number of scholars who have paid attention to the specific characteristics of medical supplies still use static Nash equilibrium solutions, unable to analyze the dynamic changes of the system. Therefore, this paper first assumes that decision-makers from both the government and enterprises are averse to disappointment, and then incorporates the delayed effect of the reserve efforts made by the government and enterprises and the attenuation characteristics of the value of emergency medical supplies. By dynamic differential game, this paper constructs a government-enterprise joint reserve model of emergency medical supplies. Then, the optimal reserve efforts, the optimal benefits of the supply chain system, and the optimal social reputation trajectory of enterprises are discussed from a dynamic perspective under a decision-making model without cost sharing, a decision-making model with cost sharing, and a centralized decision-making model. Finally, it also analyzes the impact of the degree of disappointment aversion, the value decay rate of emergency medical supplies, and the delayed effect on optimal decision-making.By comparing the results of the three decision-making models and analyzing the sensitivity of the key relevant parameters, the following conclusions can be drawn: 1) Due to the attenuation of the value of medical supplies, the optimal social reputation trajectory of enterprises initially increases over time, but gradually decreases after reaching its peak. The social reputation trajectory of the enterprise is positively correlated with the delayed time of the reserve efforts of both the government and enterprises, and negatively correlated with the degree of disappointment aversion. 2) The optimal levels of reserve efforts of both the government and enterprises are positively correlated with the delayed time of their reserve efforts, and negatively correlated with their respective degree of disappointment aversion. 3) For the benefits of the emergency supply chain system, its value is directly proportional to the delayed time of the reserve efforts of both the government and enterprises, and inversely proportional to the degree of disappointment aversion of both parties. 4) Regardless of how other variables change, the optimal social reputation of enterprises, levels of reserve efforts, and the benefits of the supply chain system in the centralized model are always greater than those of the decision-making model with or without cost sharing. In the centralized decision-making mode, the optimal decision-making of the emergency supply chain system can achieve Pareto optimality.Based on the conclusion of this paper, the following managerial insights can be obtained: Regarding the attenuation characteristics of emergency medical supplies, it is possible to consider shortening the reserve cycle and reducing material waste to maximize the value of the supplies. Although the delayed time of reserve efforts of both the government and enterprises can improve the social reputation of enterprises and the benefits of the supply chain system, its promoting effect is limited to a certain extent. Both the government and enterprises should ensure that the delayed time is maintained within an acceptable range to attract public attention to reserve efforts. In terms of the impact of the degree of disappointment aversion, it has an inhibitory effect on the social reputation of enterprises, and the negative impact on the benefits of the supply chain system is particularly serious. Therefore, decision-makers from both the government and enterprises should be able to remain rational when making relevant decisions and strive to eliminate the disappointment aversion mentality of seeking advantages and avoiding disadvantages.