Containing rumours using mathematical tools: Stripes, clusters and hotspots. The words might evoke images of wildlife habitats, or even weather maps. But according to new research, they also describe how misinformation spreads through society. According to the UN Global Risk Report 2024, mis- and disinformation is not only a top global threat—it’s the one countries feel least prepared to address.
Over 1,100 experts from 136 countries have ranked it among the gravest risks, and more than 80 per cent said it’s already happening. Recent examples of the grave consequences of misinformation include the manipulation of the 2016 US presidential election, COVID vaccine hesitancy, and the growth of QAnon.
Traditional thinking around the issue of misinformation suggests that rumours travel straight, and spread uniformly among people. Recent research, however, shows, nothing is as straight as it seems.
For one, misinformation rarely behaves ‘neatly’. Certain communities become “hotspots” where rumours intensify, while elsewhere they fade quickly. Some neighbourhoods, online groups, or communities will suddenly become flooded with misinformation, even as others remain relatively untouched.
Using mathematical models, researchers have found that rumours rarely spread evenly; instead, they organise themselves spatially. So rumours are transmitted just like ink dissolves in water, or how patterns show up on a tiger’s skin or that of the zebra, or disease outbreaks spread in a population.
Misinformation holds significant influence on multiple aspects of society such as affecting the economy by causing stock market crashes, shaping public sentiments, impacting election results in politics, creating tensions among religious groups, instigating violence, and tarnishing reputations of important personalities.
The work of the authors of this piece thus offers a “weather map” for false information, allowing governments and fact checking authorities to anticipate the dynamics of rumor dissemination, and determine how to halt its spread.
READ IApostle of easy money: Alan Greenspan and the bubble economy
How rumours travel
Falsehoods travel faster than facts, research has shown. From inciting hate and violence, undermining health science, and discrediting climate action and other government-led efforts to accelerate the sustainable development goals (SDGs), misinformation threatens every aspect of society, according to the UN.
Researchers have mainly studied rumours through the lens of psychology and sociology: why people believe in false information, and how groups influence one another. But mathematicians have taken on a different approach. They treat misinformation as a physical system — more like ink spreading through water, than a simple conversation between people.
In our work, we used a mathematical technique called the reaction-diffusion model to examine not only how rumours are transmitted, but also how they move through communities.
For instance, the “reaction” occurs when someone encounters and believes a rumour. The “diffusion” is how that rumour travels as people interact, move, and share information across social networks.
Looking at both processes together revealed something unexpected. Rumours do not spread evenly. Instead, they form patterns — clusters, stripes, hotspots and even maze-like structures — similar to the natural patterns seen in animal markings or chemical reactions. These are known as Turing patterns.
Our model also shows that where a rumour begins can shape how it spreads. A rumour that starts in one part of a network may create concentrated hotspots, while one that starts elsewhere may spread in long bands across a community. This raises the possibility of predicting where misinformation is most likely to take hold, much like a weather forecast identifies areas at risk of storms.
More importantly, the research identifies ways to disrupt these patterns. Fact-checking and trusted media interventions can act as corrective forces that weaken rumours. So can self-correction, when people realise information is false or no longer newsworthy and stop sharing it. Together, these mechanisms can break up large misinformation clusters and prevent them from spreading further.
Thus, while psychologists can explain why individuals believe rumours, treating rumours and their movement as a physical system helps explain how thousands of individual interactions combine to create a large-scale “rumour storm” — and how it might be contained before it causes real-world harm.
Containing rumours
Mathematical models have long been used to study how rumours spread. One of the earliest, the Daley-Kendall model, developed in 1964, divided people into three groups: those unaware of a rumour, those spreading it, and those who had stopped passing it on.
Such models help researchers understand the mechanisms that drive misinformation and test ways to contain it. Much as epidemiologists model disease outbreaks, scientists can use mathematics to predict how rumours will spread, identify vulnerable communities, and evaluate interventions before they are implemented.
Drawn from epidemiology, recent studies have effectively used these models — developed originally to study the spread of viruses – to study the diffusion of misinformation across social networks.
Our study builds on that tradition but adds several new elements. It incorporates media correction, self-correction, public awareness and forgetting (when people simply forget about the rumour) within a single framework. It also accounts for verification behaviour — when people stop sharing information after realising it is false or no longer newsworthy.
By gaining insights into the “patterns” of how people interact, predicting the stability of these patterns, testing the interventions, and spatially controlling rumours, mathematical models such as ours can help control the menace of misinformation.
Misinformation control cannot rely solely on deleting posts or using automated moderation systems. Social behaviour itself matters greatly. Fact-checking, trusted media communication, public awareness, and encouraging people to verify claims before sharing them may all help disrupt rumor “hotspots.”
In that sense, combating misinformation resembles public health management. Prevention, education, and community behaviour can be just as important as technological intervention.
Future studies could make these models even more realistic by incorporating actual social media data, and complex online networks. Studying how multiple rumours compete with one another, or how misinformation interacts with corrective information in real time, would also further help the cause of tackling misinformation.
Ultimately, this line of research points toward a growing scientific understanding of misinformation — not merely as random noise on the internet, but as a complex system that follows patterns, responds to interventions, and may even obey mathematical laws similar to those found in nature itself.
Ranjib Banerjee is Associate Professor, School of Business, UPES, Dehradun. Subrata Ghosh is Assistant Professor, Lodz University of Technology, Poland. Naresh Saha is Assistant Professor, School of Engineering, Dyananda Sagar University, Bengaluru. Originally published under Creative Commons by 360info
.