Information Diffusion on Instagram using SIR and SEIR Models

Social Network Analysis (SNA) studies how users interact with each other on online platforms. It helps in understanding how information moves from one user to another. Information diffusion explains how content spreads among users over time. In this study, the spread of information on social media is analyzed using epidemic models, namely the Susceptible–Infected–Recovered (SIR) model and the Susceptible–Exposed–Infected–Recovered (SEIR) model. The dataset is based on Instagram influencer data and includes variables such as the number of followers, average likes, total likes, and number of posts, influence score, and engagement rate. Since social media datasets do not directly provide SIR components, proxy variables are defined. Followers represent susceptible users, average likes represent actively engaged users (infected), and total likes per post represent recovered users. All variables are normalized to make them comparable and stable. The SIR and SEIR models are simulated for 30 days. The comparison is based on two measures: peak infection and the time taken to reach the peak. The results show that the SIR model gives higher and faster peaks. The SEIR model shows a more realistic pattern because it includes a delay in user engagement through the exposed stage. This study uses a proxy-based approach due to limited observation of actual user states. The mapping of followers, average likes, and total likes per post to SIR compartments is treated as an approximation of aggregated engagement behavior rather than exact user states. A sensitivity study is performed by varying key parameters such as the infection rate (?), recovery rate (?), and incubation rate (?). In addition, a basic empirical validation is carried out by examining the consistency between simulated diffusion patterns and observed engagement trends. The results provide a constrained but practical interpretation of information diffusion in large-scale social media environments.