Model 2:
Separating Capture from Assimilation

The SAss model demonstrated that fictional contagion could be represented mathematically using only two compartments. While elegant, it assumed that every susceptible individual became assimilated immediately after contact.

Many fictional—and real-world—phenomena, however, unfold through intermediate stages. A person may first be influenced, recruited, exposed, captivated, or infected before irreversible transformation occurs.

Model 2 introduces this missing stage.

Rather than moving directly from Susceptible to Assimilated, individuals first enter a Captured state.

This distinction transforms contagion from a single event into a multi-stage process.

Imagine several examples from the fictional worlds explored in this project.

A human captured by the Borg has not yet been fully assimilated.

A victim bitten by an aswang may still be rescued before complete transformation.

An individual recruited by an extremist group has not necessarily embraced its ideology.

Someone exposed to illegal drugs is not immediately addicted.

These examples suggest that capture and assimilation represent different biological, psychological, or social processes.

Recognizing this distinction allows the model to ask richer scientific questions.

Instead of asking only

"How does contagion spread?"

Model 2 asks

"How long does the transition from exposure to irreversible transformation take?"

That shift greatly expands the kinds of hypotheses that can be investigated.

The population is now partitioned into three compartments:

• Susceptible (S) — individuals vulnerable to capture.

• Captured (C) — individuals who have been influenced or seized but have not yet completed transformation.

• Assimilated (A) — individuals who have undergone complete transformation and can contribute to the spread of contagion.

The corresponding stock-and-flow structure is:

S --> C --> A

This simple diagram reveals an important conceptual advance.

Assimilation is no longer instantaneous.

It is the outcome of an earlier process.

The first equation tells us that susceptible individuals leave their compartment only through capture.

The second equation describes the transient nature of captivity. Captured individuals are continually entering from the susceptible compartment while simultaneously progressing toward assimilation.

The third equation shows that the assimilated population grows only through the successful completion of assimilation.

Together, these equations conserve the total population:

S + C + A = N.

No individuals are created or destroyed through contagion; they simply move from one state to another.

At first glance, adding one compartment may appear to be a small mathematical modification.

Scientifically, however, it represents a major conceptual advance.

By distinguishing capture from assimilation, researchers can now investigate questions such as:

• How quickly does assimilation occur after capture?

• Can interventions target individuals before assimilation becomes complete?

• Which process—capture or assimilation—has the greater influence on the epidemic?

Such questions cannot even be formulated within the simpler SAss model.

Model 2 demonstrates that improving a scientific model does not necessarily require making it dramatically more complicated.

Sometimes, the most significant advances come from recognizing that one process actually consists of two distinct mechanisms.

This principle extends far beyond epidemiology. It appears in ecology, engineering, economics, computer science, and many other disciplines whenever researchers decompose complex systems into interacting components.