Behavioral influences on rumor dynamics: A compartmental model with hesitation, forgetting, and self-remembering mechanisms in complex heterogeneous social networks

Rumors are informal pieces of information that can spread easily within various social networks, often leading to misinformation or misunderstandings among groups of people. Rumor diffusion depends on various factors, including individual behavior, individual psychology, network dynamics of different social networks, crisis management, etc. Understanding the rumor propagation dynamics for different human psychological mechanisms is important because they influence why people share particular information, how they evaluate rumor’s credibility and their emotional reactions. This paper introduces a rumor propagation model in a complex heterogeneous social network. To study the influence of human behavioral mechanisms on the spreading of rumor, we incorporate three key behavioral mechanisms—hesitation, forgetting, and self-remembering in our model. We prove the global stability of our model’s equilibrium points using the Lyapunov function and the LaSalle invariance principle. In numerical analysis, we study the effects of the hesitating, forgetting, and self-remembering mechanisms that offer a comparative analysis of how these factors affect the spread of rumor over time. Furthermore, we implement two optimal control strategies—InformedGuard and SkeptiShift, analyzed through Pontryagin’s Maximum Principle, demonstrating how targeted interventions can significantly mitigate rumor prevalence in heterogeneous networks. We cross-validate our numerical results against our theoretical predictions, that demonstrates consistency and provides deeper insights into controlling and mitigating rumor propagation within complex networks.