https://doi.org/10.1140/epjp/s13360-026-07381-6
Regular Article
Dynamic analysis of rumor propagation: media effect, forgetting and remembering mechanisms
1
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Chennai, Chennai, Tamil Nadu, India
2
Department of Mathematics, School of Advanced Sciences, VIT-AP University, 522241, Inavolu, Beside AP Secretariat, Amaravati, Andhra Pradesh, India
a
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Received:
5
December
2025
Accepted:
29
January
2026
Published online:
14
February
2026
Abstract
In the digital age, the rapid spread of rumors and misinformation poses significant challenges to society, shaping public perception, influencing decision-making, and undermining social stability. A comprehensive understanding of rumor propagation, particularly in relation to reporting behavior, is crucial for developing effective strategies to curb the dissemination of false information. Our study presents an in-depth investigation into the mechanisms of rumor spread, with a focus on the interplay between propagation dynamics and the reporting effect within social networks, modeled using a Holling type II functional response. In addition to media reporting, the proposed model incorporates behavioral aspects of the population, specifically the processes of forgetting and remembering, which play a vital role in the overall dissemination of rumors. Our model also accounts for individuals expressing their personal beliefs about the credibility of a rumor, thereby examining how such actions affect the speed, reach, and persistence of its spread. Due to misinformation, the public retains the incidents with a short term memory and the same fades away slowly. We incorporated the same effect through the model in accordance with to enhance the realism of the proposed framework. Our model excels and offers some deep evidence-based insights, where the model is capable of portraying the complex dynamics of rumor propagation, which will play a major role in social media reporting and behavior. Our research reveals that rumor propagation is impacted by media coverage in both directions. Rumors will spread throughout society and cause confusion, but the media can also raise awareness and lessen their negative effects. In a similar vein, forgetting and remembering mechanisms aid in limiting the spread of rumors at a specific moment. However, they can also rekindle rumors that have been forgotten due to the emergence of new ones. Also our findings highlights that a higher rumor disappearing rate reduces susceptible, confused, and infected populations and lessens the need for media intervention, which accelerates containment. Stronger dissemination, on the other hand, shortens the healing period but increases disorientation and infection peaks.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
