8.3 Spreading of Disease: A System of First Order ODEs
231
Fig. 8.12 Small outbreak of flu at a boarding school (β is much smaller than in Fig. 8.11)
or simpler
βS(0)
γ
> 1
(8.29)
to increase the number of infected people and accelerate the spreading of the disease.
You can run the SIR1.py program with a smaller β such that (8.29) is violated and
observe that there is no outbreak.
The power of mathematical modeling
The reader should notice our careful use of words in the previous paragraphs.
We started out with modeling a very specific case, namely the spreading of
flu among pupils and staff at a boarding school. With purpose we exchanged
words like pupils and flu with more neutral and general words like individuals
and disease, respectively. Phrased equivalently, we raised the abstraction level
by moving from a specific case (flu at a boarding school) to a more general
case (disease in a closed society). Very often, when developing mathematical
models, we start with a specific example and see, through the modeling, that
what is going on of essence in this example also will take place in many
similar problem settings. We try to incorporate this generalization in the model
so that the model has a much wider application area than what we aimed at in
the beginning. This is the very power of mathematical modeling: by solving
one specific case we have often developed more generic tools that can readily
be applied to solve seemingly different problems. The next sections will give
substance to this assertion.
231
Fig. 8.12 Small outbreak of flu at a boarding school (β is much smaller than in Fig. 8.11)
or simpler
βS(0)
γ
> 1
(8.29)
to increase the number of infected people and accelerate the spreading of the disease.
You can run the SIR1.py program with a smaller β such that (8.29) is violated and
observe that there is no outbreak.
The power of mathematical modeling
The reader should notice our careful use of words in the previous paragraphs.
We started out with modeling a very specific case, namely the spreading of
flu among pupils and staff at a boarding school. With purpose we exchanged
words like pupils and flu with more neutral and general words like individuals
and disease, respectively. Phrased equivalently, we raised the abstraction level
by moving from a specific case (flu at a boarding school) to a more general
case (disease in a closed society). Very often, when developing mathematical
models, we start with a specific example and see, through the modeling, that
what is going on of essence in this example also will take place in many
similar problem settings. We try to incorporate this generalization in the model
so that the model has a much wider application area than what we aimed at in
the beginning. This is the very power of mathematical modeling: by solving
one specific case we have often developed more generic tools that can readily
be applied to solve seemingly different problems. The next sections will give
substance to this assertion.