Model Continuous-Time Markov Chain untuk Penyebaran Hoaks di Media Sosial: Adaptasi Stokastik Populasi Tertutup dari Model Deterministik

Abstract

Hoaxes are non-factual information that spreads rapidly across social media, potentially disrupting social stability. Previous studies have primarily modeled the spread of hoaxes using deterministic differential equations. However, in real-world scenarios, deterministic models have a significant limitation: they fail to capture the inherent randomness that explains why a hoax might escalate uncontrollably or vanish completely without a trace. Therefore, this study develops a stochastic approach to hoax spreading involving five compartments (Ignorant, Latent, Hoax-Spreader, Debunker, and Stifler). The model assumes a closed population and is formulated using a Continuous-Time Markov Chain (CTMC). Simulation results reveal that the mean trajectory derived from 300 stochastic realizations differs significantly from the deterministic solution. The deterministic model predicts a widespread transmission whenever the basic reproduction number is greater than one. In contrast, the stochastic simulation exhibits a bimodal outcome: in the vast majority of realizations (84.3%), the hoax simply dies out, while only a small fraction leads to a widespread outbreak. These findings demonstrate that stochastic modeling provides crucial probabilistic insights into the extinction of a hoax—dynamics that deterministic models are unable to capture.