Introduction:

Is it possible to make predictions

based on mathematical models of the spread of infectious diseases? The aim of

this mathematical investigation is to show that it is possible, by taking one

disease and setting up a model of it in order to check if the proposed solution

makes sense.

I started out with a general focus on the

mathematics behind the spread of infectious diseases, which previously have

been investigated and have a general structure by which they function, the SIR

model (which I will explain in the ‘Background Modeling’ part of the essay).

After encountering difficulties, when wanting to compare the spread of two different

diseases, I knew I had to change my research question to something more

realistic, which has not been conducted yet. I changed my research question to

the following: “Would the Zobrist-created vector plague virus be able to solve

the problem of overpopulation?”

The idea for my research question

comes from Dan Brown’s novel Inferno, (which is one of my favorite pieces)

where a scientist called Zobrist, created a vector virus of plague with the

ability to sterilize a part of the population, in order to solve the problem of

overpopulation, with which he was very concerned. The disease is imaginary, however in the novel

it is presented as an infectious disease, which meant that I could try to model

it as if it were a real infectious one. I considered modeling a real disease,

however that has been previously done, so through the addition of a component

of literature to math and biology, I added an element of uniqueness.

During the course of my exploration,

as I was learning about the SIR model, previous models of diseases, and

evaluating different mathematical approaches to the problem, I found a published

work on a mathematical modeling of a zombie epidemic. This work took an

infection and modeled various situations that could occur, depending on which

way the infection develops. After finding it, I had a much clearer plan of how

I needed to structure my personal investigation in order to be able to answer

the research question. I came to an understanding that in order to decide

whether an imaginary disease would be successful in eradicating a problem of

overpopulation, one would need to split the big problem up into smaller

components: present it in various situations that the epidemic could possibly

develop into. Therefore I separated the big question into smaller parts-

specific models; and made that my final structure, inspired by the work on

zombies. My new plan was creating individual models, and evaluating each one,

in order to evaluate the success of the proposed solution. However, the work on

Zombies had no particular research question, implying that in the end while

it’s final goal was to compare the models between each other, my work’s final

aim was to pursue various possible models, evaluate each one with no

consideration or link to the other ones, and then decide, whether the proposed

solution would be a successful one or not. As a careful addition, I made sure

to make my work more personal and unique, by changing parameters, so that even

if some calculations would overlap (as in math there is a common foundation),

the final things represented would have nothing in common.

As this essay will be dealing with an outbreak

of plague with an activation to change DNA to cause sterility to the population,

in order to solve overpopulation, it is important to understand the problem

itself. Overpopulation is an undesirable condition where the existing human population

is greater than then amount Earth can physically handle. It is caused by

factors such as diminished death rate, better restorative offices, and

consumption of valuable assets.