Exploring the hidden role of stochasticity in biochemical reaction networks during infection progression
Imagine a single virus entering a human cell. This microscopic event sets in motion a complex biochemical ballet involving thousands of molecules—genes switching on and off, proteins assembling and disassembling, chemical signals flashing through molecular pathways. For decades, scientists viewed these processes through the lens of averages and predictability, using mathematical models that assumed populations of molecules behave in perfectly continuous, deterministic ways. But just as flipping a coin doesn't always yield exactly 5 heads in 10 tosses, biochemical reactions are fundamentally discrete and inherently random at the molecular level.
Randomness at the smallest scales
Complex interactions amplify randomness
Stochasticity influences infection progression
In the 1970s, scientists began recognizing fundamental flaws in deterministic approaches to biochemical modeling. The traditional method treated molecules as continuous concentrations rather than discrete entities, essentially assuming that if a reaction happens 4.27 times per second on average, we can work with that fractional value. But in reality, biochemical reactions occur in whole numbers—you can't have half a reaction between a virus particle and a cell receptor 9 .
"Inherent stochastic fluctuations in molecule numbers can change the dynamic behavior of biochemical systems both quantitatively and qualitatively" 9 .
At the heart of stochastic simulation lies a simple but powerful concept: every biochemical reaction has a certain probability of occurring in any given moment. Scientists quantify this using reaction propensities—mathematical expressions that capture how likely a specific reaction is, based on the current molecular population and reaction kinetics 9 .
The fundamental equation governing these systems is the Chemical Master Equation (CME), which describes how the probability of having particular molecular counts changes over time. Unfortunately, this equation is typically impossible to solve directly for realistic systems.
This is where stochastic simulation algorithms (SSA) come in—instead of solving the equation analytically, they use Monte Carlo techniques to simulate many possible trajectories of the system 9 .
Calculates when the next reaction occurs and which reaction it will be using random numbers.
Calculate reaction propensities
Generate random numbers for timing
Select and execute reaction
Generates putative times for all possible reactions and executes the one that occurs first.
Generate putative times for all reactions
Identify reaction with smallest time
Execute reaction and update system
While early stochastic models focused on well-mixed molecular systems, modern applications extend to population-level disease spread. Traditional epidemic models often assume everyone interacts with everyone else equally—an obvious simplification of reality. In actual human populations, contact patterns form complex networks where some individuals ("hubs") have many more connections than others 3 .
"Computer simulations of these models are, unfortunately, computationally demanding on large networks. Efficient numerical methods are thus crucial" 3 .
In September 2025, Samuel Cure and colleagues published a groundbreaking solution: the NEXT-Net algorithm 3 . This innovative approach combines the next reaction method with rejection sampling to efficiently handle both static and temporal networks (whose structure changes over time).
What makes NEXT-Net particularly powerful is its ability to simulate non-Markovian processes—systems where the timing of events depends on history, not just the current state. This is essential for realistic disease modeling, as how long someone has been infected often affects their infectiousness.
Individuals as nodes, contacts as links
Assign probability distributions to events
Next-reaction and rejection methods
Update nodes and transitions after events
This table compares the computational efficiency of different algorithms across various network sizes, demonstrating NEXT-Net's superior scaling. Simulation times are in seconds for 1000 infection events 3 .
| Network Size | nMGA | REGIR | NEXT-Net |
|---|---|---|---|
| 1,000 nodes | 45.2 | 12.7 | 3.1 |
| 10,000 nodes | 528.6 | 89.4 | 15.8 |
| 100,000 nodes | >3600 | 645.3 | 112.5 |
| 1,000,000 nodes | N/A | >3600 | 985.2 |
This table illustrates how the same initial conditions can lead to dramatically different outcomes due to random effects, based on 1000 simulations of an SIR model on a social network with R₀ = 1.8 .
| Outcome Type | Percentage | Avg. Final Size |
|---|---|---|
| Early extinction | 21% | 1 |
| Small outbreak | 34% | 8.3 |
| Large epidemic | 45% | 61.7 |
| Algorithm | Type | Scalability | Key Limitation |
|---|---|---|---|
| nMGA | Approximate | Poor for large networks | Slow with many infected nodes |
| Laplace Gillespie | Exact | Moderate | Only works for decreasing rate functions |
| REGIR | Approximate | Moderate | Approximate nature introduces error |
| NEXT-Net | Exact | Excellent (linear scaling) | Requires careful implementation |
Modern stochastic simulation relies on both theoretical frameworks and practical computational tools.
Exact simulation of reaction networks for modeling viral replication inside cells.
Efficient event scheduling using priority queues for network-based epidemic models 3 .
Faster sampling for large reaction networks in intracellular signaling pathways 6 .
Modeling sudden, dramatic environmental changes for assessing impact of superspreading events 5 .
Capturing memory effects in biological systems for modeling long-term immunity dynamics 7 .
As computational power continues to grow and algorithms become more sophisticated, stochastic simulation is moving in several exciting directions:
Connecting molecular-level events within infected cells to population-level transmission patterns.
Incorporating surveillance data to update model parameters during ongoing outbreaks.
Virtually evaluating control strategies before implementing them in the real world.
Using individual-level data to generate personalized risk assessments.
The SPEED (Stochastic Predictor of Early Epidemic Detection) model has been developed specifically for early outbreak detection and response planning, dynamically adjusting as new case information becomes available 8 .
The shift from deterministic to stochastic thinking in infectious disease modeling represents more than just a technical improvement—it's a fundamental change in how we understand biological processes. By embracing the inherent randomness of biochemical systems, from the molecular to the population level, scientists are developing more realistic models that better capture why diseases behave in seemingly unpredictable ways.
"I have come to believe that one's knowledge of any dynamical system is deficient unless one knows a valid way to numerically simulate that system on a computer" 9 .
The invisible dice that determine the fates of molecules, cells, and entire populations may never stop rolling, but through stochastic simulation, we're learning to read them better than ever before.