Dai Daoming, Wu Xuanyu, Si Fengshan
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030 China.
School of Management, Hefei University of Technology, Hefei, 230009 China.
Adv Differ Equ. 2021;2021(1):39. doi: 10.1186/s13662-020-03173-z. Epub 2021 Jan 9.
The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-19 vaccines efficiently and safely to the areas affected by the epidemic. This paper focuses on vaccine transportation in a supply chain model composed of one distributor and one retailer (clinic or hospital), in which the distributor procures COVID-19 vaccines from the manufacturer and then resells them to the retailer. Distributor detects the activity level of the vaccines, and retailer is responsible for transportation of the vaccines. Firstly, we establish a difference equations model with time-delay. Secondly, we investigate the impact of time-delay on the stability of vaccine supply chain. In addition, we explore the influence of decision adjustment speed of the distributor (or retailer) on the stability of vaccine supply chain. Finally, we verify the theoretical results by a two-dimensional bifurcation diagram, the largest Lyapunov exponent, entropy, and domain of attraction. The results show that when the decision delay-time or the adjustment speed of decision variables exceeds a certain threshold, it brings a negative impact on the stability of vaccine supply chain system. The stability domain of the system shrinks as customers' sensitivity to cold chain transportation decreases and by contrast expends as customers' sensitivity to vaccine prices decreases. When the vaccine supply chain is in a state of chaos, the effect of external control over the system is superior to that of internal control over the system.
新冠疫苗的研发受到世界各国的高度关注。截至目前，多种新冠疫苗已进入三期临床试验。然而，要将新冠疫苗高效且安全地运送到疫情受灾地区却很困难。本文聚焦于由一个经销商和一个零售商（诊所或医院）组成的供应链模型中的疫苗运输问题，其中经销商从制造商处采购新冠疫苗，然后转售给零售商。经销商检测疫苗的活动水平，零售商负责疫苗的运输。首先，我们建立一个具有时滞的差分方程模型。其次，我们研究时滞对疫苗供应链稳定性的影响。此外，我们探讨经销商（或零售商）决策调整速度对疫苗供应链稳定性的影响。最后，我们通过二维分岔图、最大李雅普诺夫指数、熵和吸引域来验证理论结果。结果表明，当决策延迟时间或决策变量的调整速度超过一定阈值时，会对疫苗供应链系统的稳定性带来负面影响。随着客户对冷链运输的敏感度降低，系统的稳定域缩小；相反，随着客户对疫苗价格的敏感度降低，稳定域扩大。当疫苗供应链处于混沌状态时，对系统的外部控制效果优于内部控制效果。
