:: Models > Model 1
What is the simplest mathematical model capable of representing a fictional contagion?
The previous page introduced a classical population model that described how a population changes naturally through time. While essential as a baseline, it did not yet describe contagion. Every individual belonged to a single population, and no interactions could transform one person into another state.
The first scientific challenge was therefore to introduce the simplest possible mechanism of transmission.
Rather than beginning with a sophisticated framework involving rescue, rehabilitation, or immunity, this project deliberately started with a minimal abstraction. Every susceptible individual could become assimilated after interacting with an assimilated individual. Nothing more.
This deliberate simplicity allowed the fundamental mechanics of contagion to be understood before additional processes were introduced.
The first question asked by the project was remarkably simple.
Can the essence of fictional contagion be represented using only two population states?
This question reflects an important principle of computational science.
Researchers rarely begin with the most comprehensive model.
Instead, they first ask whether the essential behavior of a system can be captured using the fewest assumptions possible.
Model 0 successfully described natural population growth, but it could not answer questions such as:
How quickly does fictional contagion spread?
How many susceptible individuals eventually become assimilated?
What determines whether assimilation accelerates or slows?
Can the population eventually become dominated by the assimilated?
These questions require interactions between individuals rather than simply changes in population size.
A new abstraction was therefore necessary.
The conceptual leap introduced by Model 1 is surprisingly profound.
Instead of viewing the population as a single homogeneous group, the model divides it into two distinct compartments:
Susceptible (S) — individuals who have not yet been assimilated but are vulnerable to contagion.
Assimilated (Ass) — individuals who have already undergone transformation and are capable of assimilating others.
This is the first appearance of the compartmental modeling philosophy that eventually grows into the SCARED framework.
One of the most powerful ways to understand a complex system is to partition it into meaningful states. Rather than treating every individual independently, compartmental models group together individuals who share the same characteristics. The complexity of individual behavior is replaced by the simpler dynamics of transitions between states.
Compared with Model 0, only one new idea has been introduced.
The addition appears almost trivial.
Yet this single transition transforms a population model into a contagion model.
The remainder of the research can be viewed as a systematic exploration of what additional transitions are required to better represent recoverable real-world systems.
Each equation describes the rate at which one compartment changes through time.
The susceptible population decreases as individuals become assimilated.
Conversely, the assimilated population increases through exactly the same process.
The equations therefore express a conservation principle:
Every individual who leaves the susceptible compartment appears in the assimilated compartment.
Nothing is created.
Nothing is lost.
Individuals simply change state.
Viewed today, the SAss model appears almost deceptively simple.
Yet its simplicity was intentional.
Every later model in this archive—including SCA, SCAR, SCARE, and SCARED—can be understood as successive refinements of this initial abstraction.
Rather than attempting to represent every possible process simultaneously, the research began with the smallest model capable of exhibiting contagion.
In retrospect, this decision illustrates a central principle of computational science:
Complex models are most reliable when they evolve from simpler ones whose behavior is already understood.
The idea of partitioning a population into compartments has a long intellectual history. Early epidemic models, most notably the seminal work of William Ogilvy Kermack and Anderson Gray McKendrick in 1927, demonstrated that disease dynamics could be understood by dividing populations into distinct epidemiological classes and describing the rates at which individuals move between them.
Model 1 follows this tradition while introducing a different interpretation of contagion. Instead of representing biological infection, assimilation serves as a generalized metaphor for irreversible transformation, whether brought about by fictional species or analogous real-world processes. In doing so, the model takes the first step toward extending classical epidemiology beyond infectious diseases into the broader study of generalized contagion.
Suppose this were the only model available.
What important aspects of real-world contagion would still be missing?
Consider questions such as:
Must assimilation occur immediately after contact?
Is every captured individual inevitably assimilated?
Could intervention occur before transformation becomes permanent?
Are all assimilated individuals equally capable of influencing others?
Recognizing these limitations naturally leads to the next conceptual advance.
The next model asks a deceptively simple question:
What happens if capture and assimilation are treated as two separate processes?
That question gives rise to Model 2: Separating Capture from Assimilation.
A phenomenon becomes computationally understandable when we stop describing individual objects and begin describing the states they can occupy and the transitions between those states.
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