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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.

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 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.

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