Formation and Dynamics of Donation on Social Networks in the Post-Epidemic Era

The characteristics of donation during the COVID-19 breakout in Shanghai in 2022 are obviously different from those in Wuhan in 2020, and this article aims to explore the formation and dynamics of donation in the post-epidemic era. This article uses the scale-free network to describe the structure of a society. There are four types of players in our model based on reality: donors, illegal beneficiaries, legal beneficiaries, and inactive people. Then, this article gives and explains the benefits of four types of the scale-free network with several innovations. By the pair approximation, this article introduces the proportion of edges starting from some type of players as the population state. Based on the fast and slow system and under the weak selection, this article shows that the evolutionary dynamics of the population can be approximated by the slow system, which is a system of differential equations of the population state. Then, this article defines the equilibrium of the approximate dynamics as the global equilibrium of the population and further defines its stability. Because the analytical expressions of the global equilibrium are very complex, this article analyzes and seeks the influence of various parameters by simulation. Our conclusions reveal the evolutionary characteristics of donation in the post-epidemic era and thus give management suggestions to motivate donations and achieve a better society in different situations.