What Do Broadcast, Diffusion, and SIR Models Reveal About Article Virality?

For over half a year the author has been publishing daily articles, not only to promote the practice of mathematical modeling but also to reflect on the data behind article readership.

Broadcast Model

The initial wave of an article’s dissemination—through social media, subscription notifications, and similar channels—is modeled as a broadcast. Let N(t) be the number of readers at time t , S(t) the potential readers who have not yet encountered the article, and p the broadcast probability representing the strength of the spread.

When an article is first posted, the primary audience consists of followers, friends, and family; a certain proportion reads it on the first day. As time passes, the pool of potential readers shrinks, slowing the spread, which explains the early surge in views followed by a plateau.

To increase the initial propagation speed, ensure the article is visible to as many people as possible immediately—through push notifications, community sharing, or friend forwarding—to raise the broadcast probability.

Diffusion Model

Beyond the initial push, an article’s chance of becoming a “viral hit” depends on word‑of‑mouth sharing among readers. The diffusion model captures this secondary spread.

In this model, let N be the total relevant audience and β the diffusion probability, indicating the likelihood that each reader shares the article with others.

Readers become active nodes in the propagation chain, forwarding the article to social circles, groups, or personal contacts, thereby re‑activating the spread.

Each share expands the article’s influence, reaching readers outside the original circle. Emotional resonance, practical value, and controversial topics typically increase the diffusion probability.

Personal observation shows that articles containing personal stories or emotional connections tend to spread more widely than purely technical pieces.

SIR Model

Even the most popular articles eventually lose momentum. The SIR model, originally from epidemiology, is now widely applied to information diffusion.

The audience is divided into three groups: Susceptible (those who have not read the article), Infected (currently reading and potentially sharing), and Recovered (lost interest and no longer sharing).

The key formula is the basic reproduction number R₀ = (β × contact probability) / recovery probability . When R₀ > 1 , the article spreads rapidly; when R₀ < 1 , the spread slows and eventually stops. A low R₀ explains why some articles experience a quick decline in attention.

Adjusting content to keep readers engaged can raise R₀ , sustaining the article’s heat longer.

Understanding these mathematical models provides practical guidance for improving article reach and longevity.

Thank you to all readers for their support; I hope this sharing offers a fresh perspective on the mathematics of information diffusion.

Reference: Scott Page, Model Thinking: How Data Analysis Shapes Our Understanding , Zhejiang Science & Technology Press, 2023, p.565.