A recent research introduces a hybrid SIS (Susceptible-Infected-Susceptible) model that combines continuous epidemic dynamics with discrete demand spikes to accurately predict user engagement patterns in frequently updated software products like video games.
In a world of constant software updates, predicting how users will react can feel like chasing a moving target. Whether it's a live-service video game or your favorite productivity app, updates can suddenly spike user activity. But what if we could predict that behavior as accurately as we model the spread of a virus?
That’s exactly what a team of engineers at Purdue University set out to do. Their recent paper, Hybrid SIS Dynamics for Demand Modeling of Frequently Updated Products, introduces a smart way to model user demand using a combination of continuous epidemic modeling and discrete update “shocks.”
Software products—especially games—have user bases that grow and shrink over time. Think of a new in-game season, a bug fix, or a feature drop. After these updates, there's often a sudden surge of interest, followed by a gradual tapering off.
Instead of guessing what will happen, engineers turned to the SIS epidemic model, which stands for Susceptible-Infected-Susceptible. This is usually used to track how diseases spread, but here, “infection” represents users actively using the product.
Traditional models like SEIR can’t handle systems where people stay “infected” (i.e., engaged) indefinitely. But in software, that’s exactly what can happen: people may stop playing a game and come back again later—maybe even forever!
That’s why the researchers developed a Hybrid SIS Model that combines:
Let’s break it down simply:
Between updates, user activity follows a curve:
This is modeled with two parameters:
At each product update (e.g., new season), there's an instant jump in users: Think of this as a burst of "excitement" pushing more people to use the app.
This spike is modeled using α (alpha), a scaling factor that boosts current user engagement.
The model toggles between these “modes” depending on when an update is released.
The team tested this model on real player data from the game Apex Legends. They looked at daily peak player counts from November 2020 to February 2023 and marked key update dates.
And it worked! The simulated curves closely followed the actual player behavior, proving the model’s accuracy.
To ensure their model wasn’t just a fluke, the researchers threw a few curveballs at it:
They created clean, ideal data and tested the estimation process. The model predicted behavior almost perfectly when time steps were small.
They added "realistic" noise (like measurement errors or random fluctuations). The accuracy dropped a bit, but it still managed to predict key trends—especially the reproduction number (β/γ), which shows how fast engagement spreads.
They added randomness to how user interest grows or fades over time. Even with that, the model was surprisingly stable.
This hybrid model is a powerful tool for understanding and predicting how users respond to software updates. Here are the key takeaways:
The paper ends with exciting ideas for future improvements:
Incorporating seasonal patterns (weekends vs. weekdays) could improve prediction accuracy even further.
Using Bayesian methods or machine learning might help estimate parameters even with messy or sparse data.
What if users were modeled as different groups, like hardcore gamers vs. casuals? This could offer a richer view of demand.
Eventually, this model could power live dashboards for software companies to track and forecast engagement in real time!
Why does this matter for engineers and product teams?
Modeling user behavior may sound like sociology or psychology—but this research shows it’s also a precise engineering challenge. By merging epidemic theory with real-world data, the team gives us a new lens for understanding digital engagement.
SIS Model (Susceptible-Infected-Susceptible) - A way to model how something spreads—like a virus or trend—where people (or users) can become "infected" (engaged), recover (lose interest), and get re-infected again.
Engagement Rate (β or Beta) - This tells us how quickly people start using the product—higher beta means more people are getting "hooked" fast!
Disinterest Rate (γ or Gamma) - This shows how quickly people stop using the product—higher gamma means users lose interest more quickly.
Impulse Event (α or Alpha) - A sudden boost in user activity, like a big update or new game season—alpha measures how big that spike is.
Continuous-Time Dynamics - A way of modeling things that change smoothly over time—think of a graph with a flowing curve.
Discrete-Time Event - Something that happens all at once at a specific time—like flipping a switch or launching an update.
Parameter Estimation - The process of figuring out the values of β, γ, and α from data—like tuning your model to fit real-world behavior.
Reproduction Number (R₀ = β/γ) - A fancy way of saying how contagious the trend is—if R₀ is high, engagement spreads quickly and sticks around!
Noise - Random errors or fluctuations in the data—just like static on a radio—it can be from measurement errors or unpredictable user behavior.
Hybrid Model - A model that combines two styles—smooth, continuous behavior and sudden jumps—to capture complex real-world patterns.
Ian Walter, Jitesh H. Panchal, Philip E. Paré. Hybrid SIS Dynamics for Demand Modeling of Frequently Updated Products. https://doi.org/10.48550/arXiv.2506.01866
From: Purdue University.
