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How does a population change through time when no fictional contagion is present?
When people hear the phrase epidemiological model, they often think immediately of disease transmission. However, before one can study the effects of infection, assimilation, rescue, rehabilitation, or resistance, it is necessary to understand how the population behaves in the absence of these processes.
This idea is fundamental throughout science. Researchers first establish a baseline condition and then measure how additional factors alter that baseline. In this project, the baseline is represented by a classical population dynamics model describing the natural growth and decline of a population over time.
Model 0 therefore serves as the reference point for all subsequent models in the archive. Every fictional epidemic introduced later can be interpreted as a modification of this underlying population system.
The earliest population models sought to answer a deceptively simple question:
If a population reproduces continuously, how will its size change through time?
Although simple, this question lies at the heart of ecology, demography, epidemiology, and many other scientific disciplines.
Long before researchers studied the spread of diseases, they first sought to understand the dynamics of populations themselves.
One of the earliest mathematical descriptions of population growth is attributed to the English scholar and economist Thomas Robert Malthus.
In his influential work, An Essay on the Principle of Population, Malthus proposed that populations tend to grow geometrically when resources are abundant. Although later models introduced additional complexities and limitations, the Malthusian model established an important scientific principle:
Population change can be described mathematically.
This idea eventually became one of the foundations upon which modern population dynamics and epidemiological modeling were built.
Before modeling a complex system, scientists often begin by modeling a simpler version of the same system. This process establishes a baseline against which more sophisticated models can later be compared. Understanding the simplest case is frequently the first step toward understanding more complicated phenomena.
Let:
N(t) be the population size at time t,
r be the intrinsic growth rate of the population.
The classical exponential growth model is:
dN/dt = rN
This equation states that the rate at which the population changes is proportional to the current population size.
Although compact, the equation expresses a powerful idea.
The term N represents the number of individuals currently present.
The parameter r represents the tendency of the population to grow (or decline).
The derivative dN/dt measures how rapidly the population changes through time.
The equation therefore states:
The larger the population becomes, the more individuals are available to contribute to future growth.
This self-reinforcing process leads to exponential growth when r > 0.
At first glance, this model appears unrelated to vampires, zombies, Borg invasions, or aswangs. Yet it provides the foundation upon which all subsequent models are built.
Every compartment introduced later—Susceptible, Captured, Assimilated, Rescued, Educated, and Defiant—represents a subdivision of the population whose dynamics ultimately depend on the same principles of population change.
In this sense, Model 0 is the soil from which the entire model family grows.
Viewed in isolation, Model 0 is simply a classical population model. Viewed within the broader context of this project, however, it serves a deeper purpose.
It establishes the baseline world before contagion.
Only after understanding this world can researchers meaningfully ask what happens when fictional epidemics, social contagions, or behavioral influences begin to spread throughout the population.
The later models in this archive therefore do not replace Model 0. They extend it.
Consider the following questions:
Is exponential growth a realistic assumption for human populations?
How might limited resources alter the model?
Would a logistic growth model be more appropriate?
How would age structure, migration, or spatial distribution affect the dynamics?
What happens when fictional contagion is introduced into a population that is already changing naturally?
These questions lead naturally to the next stage of the archive:
What happens when population growth alone is no longer sufficient to explain the system?
That question gives birth to Model 1: The Simplest Contagion.
Before scientists can understand change, they must first understand what happens when nothing disturbs the system.
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