传染病防控下的市民慢性病药品现场购药需求的周期优化

doi:10.12082/dqxxkx.2021.200189

摘要/Abstract

摘要：

呼吸道传染疾病在人群间的传播,容易引发大规模的公共卫生事件。在疫情防控期间,通过限制购药周期可以有效控制和降低因购药聚集而产生的感染风险。本文聚焦传染病疫情防控中封闭与复工初期慢性病患者的购药需求,针对到店购药场景,提出一个慢性病患者购药周期的优化方法。首先,依据武汉市疫情防控期间“不得跨区购药”的原则,通过复杂网络模型,构建药店与小区之间可能的服务关系;然后基于共享单车订单数据提取购药人流量随距离的衰减规律,在此基础上建立小区购药人流在为其提供服务的各药店间的分配机制,进而确定药店侧的顾客到达速率,实现小区和药店的空间分布特征与排队论模型的耦合;接着采用离散事件仿真方法对不同购药周期下的系统状态进行仿真;最后基于仿真结果,以最大程度地兼顾患者的购药需求和药店的使用率为优化目标,通过二分法查找购药周期的最优解。实验以武汉市中心城区为例,首先通过条件概率估算各类慢性病患者的数量,再通过上述方法求解得到最优购药周期为28 d。该周期下,患者的人均等待时长为8.55 min,接近最佳的排队容忍时长,绝大多数的购药需求能够被满足,且药店资源能够得到充分利用（达到繁忙状态的药店比例达到87%以上）,药店的日均备货量不超过100（瓶或盒）,处于药店备货能力范围之内。本文的方法和结论,可用于指导慢性病患者的购药决策及药店的慢性病备药。

关键词: 呼吸道传染疾病, 慢性病, 排队论, 复杂网络, 离散事件仿真, 二分法, 周期, 优化

Abstract:

The spread of respiratory diseases among people is likely to cause large-scale public health events. During the epidemic prevention and control period, the risk of infection caused by the accumulation of drug purchase can be effectively controlled and reduced by restricting the time cycle of drug purchase. This paper focuses on the drug purchase needs of patients with chronic diseases at the early stage of closure and resumption of work in the epidemic prevention and control period and proposes an optimization method for the time cycle of drug purchase according to the scene in the drugstore. First of all, according to the principle of "no drug purchase across districts" during the epidemic prevention and control period in Wuhan, the possible service relationship between the drugstore and the community was constructed through a complex network model. Then, based on the order data of Shared bikes, the attenuation law of the drug flow along with the distance was extracted, and on this basis, the distribution mechanism of the drug flow in the community was established among the drugstores providing services for it, so as to determine the customer arrival rate at the pharmacy side and realize the coupling of the spatial distribution characteristics of the community and the pharmacy with the queuing theory model. Additionally, the discrete event simulation method was used to simulate the system state under different time cycles of drug purchase. Finally, based on the simulation results, the optimal time cycle was found by using dichotomy to maximize the consideration of patients' demands for drugs and the utilization rate of drugstores. In our study, we took Wuhan central city as an example. First, the number of patients with various chronic diseases was estimated through conditional probability, and then the optimal drug purchase cycle was obtained by using the above method for 28 days. Under the optimal time cycle, the patient's average waiting time was 8.55 min, close to the optimal duration of waiting, and the vast majority of purchasing medicine needs can be met. Also, drugstores can be fully used (More than 87% of drugstores were busy), and the daily stock quantity of drugstores was not more than 100 (bottle or box), which was within the drugstore's capacity. The methods and conclusions of this paper can be used to guide the purchasing decisions of patients with chronic diseases and the preparation of chronic diseases in drugstores.

Key words: respiratory infections, chronic diseases, queuing theory, complex network, discrete event based simulation, dichotomy, cycle, optimization

王晓凡, 方志祥, 仲浩宇, 邹欣妍. 传染病防控下的市民慢性病药品现场购药需求的周期优化[J]. 地球信息科学学报, 2021, 23(2): 307-317.DOI:10.12082/dqxxkx.2021.200189

WANG Xiaofan, FANG Zhixiang, ZHONG Haoyu, ZOU Xinyan. Periodic Optimization of Drug Purchase Needs on Site for Chronic Diseases under the Epidemic Prevention and Control[J]. Journal of Geo-information Science, 2021, 23(2): 307-317.DOI:10.12082/dqxxkx.2021.200189

图/表 19

图1

表1

式（1）—式（7）中已知参数取值

参数	含义	取值
$P (A ? B ? C)$	患三类病	0.2912^[12]
P(A)	患高血压	0.2145^[12]
P(B)	患糖尿病	0.1050^[13]
P(C)	患冠心病	0.0540^[14]
$P (A \| B)$	高血压患者患有糖尿病	0.4000^[15]
$P (A \| C)$	高血压患者患有冠心病	0.7000^[16]
$P (C \| B)$	冠心病患者患有糖尿病	0.1670^[17]

表1

表2

顾客到达行为决策规则

组合规则	顾客行为
$S state = 0$ 且 $N = 1$	被服务
$S state = 0$ 且 $N > 1$ 且 $L + N < L max$	被服务+排队
$S state = 0$ 且 $N > 1$ 且 $L + N > L max$	被服务+排队+离开
$S state = 1$ 且 $L < L max$ 且 $L + N < L max$	排队
$S state = 1$ 且 $L < L max$ 且 $L + N > L max$	排队+离开
$S state = 1$ 且 $L = L max$	离开

表2

图2

图3

表3

表4

表5

表6

表7

不同患病情况的出现概率及患者数量

患病情况	概率标记	概率取值	患病人数/万人
仅患有高血压	$P A ?$	0.14921	149.21
仅患有糖尿病	$P B ?$	0.06050	60.50
仅患有冠心病	$P C ?$	0.01370	13.70
同时患有高血压和糖尿病	P(AB)	0.04200	42.00
同时患有高血压和冠心病	P(AC)	0.03780	37.80
同时患有糖尿病和冠心病	P(BC)	0.01701	17.01
同时患有高血压、糖尿病和冠心病	P(ABC)	0.01451	14.51
总计		0.33473	334.73

表7

图4

图5

图6

表8

表9

图7

表10

图8

表11

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FID	楼层数	建筑面积/m²
0	16	1267.8
1	16	18 485.4
2	16	10 595.3
…	…	…

FID	小区名称	人口数/人
1	027社区	5939
2	08经典	5619
3	122社区冶建花园东区	7567
…	…	…

城区	名称	X	Y	地址
洪山区	美佳康大药房（钢花南苑东南）	…	…	友谊大道1062号附近
汉阳区	中联大药房（江城明珠店）	…	…	四新地区管委会四新南路江城大道江城明珠
江汉区	武汉城镇职工医疗保险定点药店	…	…	新湾五路与新湾路交叉口东150 m

订单编号	用户ID	单车ID	起点X	起点Y	终点X	终点Y
275	29360203	1477421	…	…	…	…
292	48853194	1477421	…	…	…	…
317	65913653	1477639	…	…	…	…

	平均队列长度L/人	人均等待时长W/min
Little公式	0.17	6.18
仿真结果	0.10	3.80