A Mathematical Model for the Growth Dynamics of Demand in the Fashion Industry within the Era of the COVID-19 Pandemic

Abstract

The outbreak of COVID-19 infection and its effects have not spared any economy on the globe. The fourth variant has just announced its appearance with its high death toll and impact on economic activities. The basic reproductive number $\left(R_0\right)$ , which measures the transmission potential of an infectious disease, is extremely important in the study of epidemiology. The main purpose of this study was to derive $R_0$ and assess the stability of the model around its equilibrium points. The motivation was to simulate the effect of COVID-19 on the demand for fashion products and how its application has impacted the COVID-19 pandemic. A five-compartment susceptible-infection-recovery-susceptible-based model was formulated in an integrated environment with application of fashion-based personal protective equipment (FPPEs) and government policy regulation, using ordinary differential equations. Solution techniques included a mix of qualitative analysis and simulations with data from various publications on COVID-19. The study revealed that the disease-free equilibrium was both locally and globally asymptotically stable (LAS and GAS) for $R_0\le 1$ , while the disease-endemic equilibrium was both LAS and GAS for $R_0\ge 1$ . As the demand for FPPEs increases, $R_0$ decreases, and vice versa. The sensitivity analysis indicated that $R_0$ was very sensitive to the rate of application of FPPEs. This confirms the significance of high demand for FPPEs in reducing the transmission of COVID-19 infection. Again, the pandemic has had both positive and negative impacts on the demand for fashion products; however, the negative impact outweighed the positive impact. Another discovery was that government policy stringency was significant in increasing demand for FPPEs. The sensitivity analyses suggested prioritization of FPPEs application together with all recommended PPEs. We recommend inter alia that FPPEs be used together with other nonpharmaceutical interventions. Operators in the fashion industry must be dynamic in adjusting to the new trends of taste for fashion products. Finally, governments should maintain high policy stringency.