Complexity analysis of cold chain transportation in a vaccine supply chain considering activity inspection and time-delay

• Published in: Advances in difference equations Vol. 2021; no. 1; p. 39
• Main Authors: Dai, Daoming, Wu, Xuanyu, Si, Fengshan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Bifurcation theory; Chaos; Cold chain transportation; Control systems; Coronaviruses; COVID-19; Customers; Delay; Difference and Functional Equations; Difference equations; Distributors; Domains; Functional Analysis; Inspection; Liapunov exponents; Mathematical Models of Infectious Diseases; Mathematics; Mathematics and Statistics; Neimark–Sacker bifurcation; Ordinary Differential Equations; Partial Differential Equations; Sensitivity; Stability; Supply chains; Time-delay; Transportation; Vaccine supply chain; Vaccines; Cold chain transportation; Neimark–Sacker bifurcation; Chaos; Vaccine supply chain; Time-delay
• ISSN: 1687-1839; 1687-1847; 1687-1847
• DOI: 10.1186/s13662-020-03173-z

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.