{"title":"Complexity analysis of cold chain transportation in a vaccine supply chain considering activity inspection and time-delay.","authors":"Daoming Dai, Xuanyu Wu, Fengshan Si","doi":"10.1186/s13662-020-03173-z","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"39"},"PeriodicalIF":4.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7794647/pdf/","citationCount":"19","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-020-03173-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/1/9 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 19
Abstract
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.
期刊介绍:
The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions.
The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between.
The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations.
Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.