ISPR: A rumor propagation model based on dual transmission modes of friends and recommendation

Previous rumor propagation models are mostly based on friend-to-friend mechanisms or solely focused on platform recommendation mechanisms, neglecting the coexistence of these two propagation patterns in real scenarios. Considering this issue, promotion nodes are introduced to construct an ISPR (Ignorant-Spreader-Promotion-Removed) model. First, the basic reproduction number R<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is calculated using the next-generation matrix and the stability of the model at the rumor-free equilibrium point is demonstrated. Then, through numerical simulations, the theoretical findings are validated and the factors influencing rumor propagation are analyzed. The results indicate that incorporating a recommendation mechanism significantly accelerates the spread of rumors, increases the peak of rumor propagation, and expands the influence of rumors compared to traditional friend-to-friend propagation models.