Abstract: Infectious disease epidemic is the most devastative and disastrous public health emergency according to the greatest impact on public health security. In recent years, the outbreak of SARS, Ebola virus, MERS-CoV, COVID-19, Mpox, H1N1 and H1N9 have posed great threats to health threats, economic losses, psychological suffering and so no. In response to the infectious disease, prompt medical relief supplies are the key to reducing the damage. The rapid spread of infectious diseases is likely to cause the dilemma of soaring demand and shortage of medical supplies. Therefore, to rationally allocate the limited medical supplies, it is necessary to precisely forecast the demand of medical supplies in different epidemic areas.
The most used method to predict the demand for medical supplies is a two-stage method. First, a model is built to predict the spread scale of infectious diseases and determine the number of infected people, and then the demand for medical supplies is predicted. In the two-stage method, the infectious disease transmission model is critical. There is a mutual feedback relationship between the demand of emergency medical supplies and the scale of infectious disease transmission, but the infectious disease transmission model proposed does not consider the reciprocal feedback relationship.
In this paper, we construct a modified SEIAR model in which we set parameters for the effects of medical supplies, as well as quarantine measures. The modified SEIAR model can describe the influence of the medical supplies demand satisfaction on the number of infected people. According to the model, we derive the expressions of control regeneration indicators R_c, which can reflect the effectiveness of infectious disease control measures. Then, from the perspective of optimal control, we calculate the minimum satisfaction rate of emergency medical supplies demand under different quarantine proportions for the purpose of controlling the large-scale spread of the epidemic. Additionally, we conduct a sensitivity analysis of key parameters, and give suggestions on the dispatch of emergency medical supplies. In order to verify the validity of the modified SEIAR model, we conducted a case study of the COVID-19 outbreak in Wuhan in 2020. The mean absolute deviation of this model is 0.06, which proves the accuracy of the modified model. Furthermore, the results show that when the quarantine ratio p=0, the demand satisfaction rate of emergency medical supplies m=1, and the control regeneration number R_c could only be reduced to 2. 78. It means that the epidemic could not be controlled by using medical supplies without quarantine measures. When p=0.8 and m=0.55, R_c=1. That means when the quarantine ratio reaches 0.8 and the material demand satisfaction rate reaches 0.55, the epidemic can be controlled. This result can provide reference for management departments to formulate scientific medical supplies allocation targets in the situation of severe shortage. Moreover, according to the sensitivity analysis results, we can get conclusions that: (1)In case of serious shortage of emergency medical supplies, the satisfaction rate of all demand points for emergency medical supplies can be appropriately reduced based on the implementation degree and effect of quarantine measures. (2)Considering the reserve and financing situation of different kinds of medical supplies, the reasonable combination of the three kinds of supplies should be selected to meet the demand rate, and when the epidemic prevention effect of a certain medical material is outstanding, the demand for the material should be met as far as possible. The above conclusions can provide reference for management departments to formulate emergency medical supplies financing plan when facing the dilemma of shortage and a sharp increase in emergency medical supplies.

Key words: medical supplies demand, modified SEIAR model, optimal control, sensitivity analysis, epidemic

摘要： 传染病疫情的快速传播,极易面临医疗物资严重短缺的困境。针对医疗物资需求与疫情传播规模之间的相互反馈关系,构建同时考虑三种医疗物资使用效果和隔离措施实施效果的改进SEIAR传染病模型,从最优控制角度研究不同隔离比例下,为控制疫情大规模传播,医疗物资需求满足率需达到的最低水平。以2020年武汉新冠疫情为实例研究,结果显示当不采取隔离措施时,医疗物资需求满足率达到1,也无法控制疫情大规模传播;当隔离比例达到0.8时,医疗物资需求满足率达到0.55,即可控制疫情大规模传播。以上结论说明结合一定的隔离措施,不完全满足医疗物资的需求,也可取得较好的防疫效果。该研究可为相关部门在应急医疗物资严重短缺时制定物资筹措目标提供参考。

关键词: 医疗物资需求, 改进SEIAR模型, 最优控制, 敏感性分析, 传染病疫情