Instituto Tecnológico y de Estudios Superiores de
Monterrey. Campus Ciudad de México.
Proyecto Final
Dinámica de Sistemas
Professor:
Introduction
Purpose
The purpose of the model is to explain how does the Black Death behaved back in
the 1346-1353, So that people can understand what happened in that time and
why does this disease
Structure
The structure will be, by creating a complex model, using as starting point the
different ways to transmit the disease, then explaining the different process that a
person could have after getting the disease, it could be, Dying, Recovering, or
Quarantine and then Dying or recover.
Expected Results
The results that we are expecting is that our model can show us how devastating it
was for the whole world the Black Death. By showing that there was a very few
amount of people that could recover by themselves or after the quarantine, most of
them died because there was not enough technology in that time for developing a
vaccine against the plague. In addition to it, the disease was unbelievably
infectious, so even nowadays if it’s not treated as soon as the symptoms show up
the survival possibilities are on a low scale from 8-10%.
Situation under study
Background info
The Black Death has been the most devastating plague in all the history, it is
estimated that from 75 to 200 million people died during 1346 to 1353 because of
this disease.
It was originated in the arid plains of Central Asia. Therefore, it started to spread,
first trough the silk road, then trough the Mediterranean and finally it affected all
Europe but Poland, it is estimated that this disease killed between 30% and 60% of
the entire population of Europe.
The main symptoms are the appearances of buboes (This is a particular symptom
of only the plagues, gonorrhea or tuberculosis. It usually appears under the armpit,
in the groin or on the neck and it looks just like in the “image 1”.
Causes:
It doesn’t exist a real explanation of where does the plague started, but the main
theories are that the oriental rat flee. That is a specie that is the main reason for
the propagation of the Yersinia Pestis disease, it is supposed that the outbreak
begun in the south of China.
Supposedly it begun because the Chinese buried the people on the walls or on the
ground, but it was an accessible spot for the rat that was mentioned previously. So
this rat was the main source of the propagation of the disease. People could get
the virus by 2 different ways. The first one is through the air, and the second one
through skin contact.
The main reason of why does the people was infected so quickly was because in
that century the people’s hygiene was very bad, all the streets were dirty, every
kind of animals were allowed to live among them, and people were not used to
take care of themselves.
Data
The data we have is:
Number of deaths: 75 to 200 million
Period: 1346-1353
Rate of deaths: 30-60% of Europe total population
Problem Description
Danger
Actually this has no danger on people, because this plague doesn’t exist
nowadays, but on the medieval age, it was very dangerous, because the
propagation of the disease was very fast, it causes death in a short period of time,
and there were very few treatments for this disease.
Difficulty
As mentioned before, the difficulty of creating this model is very high, because is
very difficult to find accurate data about the plague, because it has been 667 years
since it happened, and in that time, very few people registered numbers of the
plague. So we are based on assumptions that a lot of researchers had done.
Problem needed to be addressed
The main point of the model is to show all the persons who read it, how does this
disease affected the people, and probably to explain how does technology and
hygiene has change in this years.
Objective
Policy Making
First of all, we can observe that the leverage points that affect our model are: contact
rate, infectivity, air infection rate, quarantine contact, time to quarantine, average
duration of infectivity, and recovery rate.
Once we defined our leverage points, we were able to determine policies in order to
have better information and to manage in a more accurate way the epidemic, which
in our case is the Black Death.
As we previously mentioned, the Black Death infectivity was really high with a rate
of .25 in each of the infection ways; moreover, once the person was infected, the
chances to survive were pretty low as the death rate of the already infected people
was also of 0.5. Also, as we described in the context information, this epidemic killed
almost 2/3 of the entire European population. In our model, we represented this
situation and we can observe graphically the effects and causes of each behavior.
Therefore, analyzing our graphs we reached a series of policies that would have
helped to stop the mortality of this epidemic:
-Firstly, the most representative factor for the disease to spread was the contact rate;
as the infectivity was high and the contact rate too, this was the main factor towards
the fatal results that it caused all over Europe. Our policy is to avoid contact rate. We
cannot change the infectivity rate as we cannot control and manipulate the virus. So
our strategy is to maintain the population under severe standards of hygiene and
also not to kiss and avoid physical contact. If we would be able to reduce at least .1
of the contact rate, the infection rate would decrease significantly.
- Then, we have the air infection rate.
The policy we decided regarding this
characteristic was that as it´s also a controllable leverage point, we can decrease it
by generating more hygienic habits. Habits such as cleaning more constantly, having
a better control of waste substances and so on.
- Third, the infected people from the quarantine. This feature we created a policy that
decrease this rate. The action would be by having better infrastructure or at least a
better control. We decided to isolate the quarantine people at least 1 km away from
the villages, just as the contemporary movies. By this action, we expect the rate to
decrease.
-Finally, we must mention that the recovery rate was very difficult to increase as we
would be talking about the creation of medicine. With today´s technology advances
and development, we would be able, through penicillin, to increase this rate and by
this action we would decrease death people.
Concluding the policy making, we can say that following our policies, the epidemic
would be significantly less mortal. The system dynamics totally help us to better
understand and have a better perspective of the behavior of the elements and how
the relationship among them generate the behavior of the graphs. Therefore, we
were able to create the policies for the good of the population.
Leverage Points
As mentioned before we identified a few important leverage points that affect the
model throughout its development.
We will now show when manipulated how this leverage points affect the entire
system.

Fractional Air infection Rate: when moving it up to zero we realized how the
black death would had been a little less lethal by killing 12million less people
on that time.

When moving the contact rate we found that it wasn’t as significant as we
thought because increasing or decreasing it didn’t make any significant
changes to the model.

As we expected if we moved the total population upwards or downwards we
would obtain a bigger number of deaths and infected people (when moved
upwards) or a lower one (when backwards)

When moving the asymptomatic and the symptomatic infectivity we realized
that the number of deaths would remain the same, supporting on that, we
can say that the disease reached its peak.

One of the leverage points that affects the most the model is the incubation
period. Which apparently affects proportionally the deaths as its
manipulated upwards.

As a contrary belief, the amount of infected people put into quarantine would
affect the most by killing them in a higher rate than if not.

Furthermore if the time to quarantine increases the number of deaths are
decreased

The variable time to die when manipulated upwards increased the life
expectancy of infected people.
Modelling
Model
Equations
Results obtained
On susceptible population the table capture shows how the population
decreased as time passed by
By reviewing the results obtained from the infectious population we could
see how it increased over time
On the other hand by checking the symptomatic infectious population, we
got to see how it increased as time passed by as the previous one.
By reviewing the death people stock we can see how it increases
dramatically as time passed by.
Unfortunately the people who got into quarantine decreased even though at
the beginning people on quarantine zone increased.
With the recovered population rate we can see the people who were not
infected and the people who were lucky enough to survive this terrible
disease. We can see how the number increases on the next capture:
Graphics
Susceptible Population
By looking at this graph we can se that as time passes the number of people
who are susceptible decreases, this may be caused of the number of people
left who are alive and the number of people who haven’t had the exam yet.
Infectious population
On the graph above we can see how people has disappeared or died with the
disease.
Symptomatic Infectious Population
The number of people infected with showing symptoms, are in the beginning
quite a few because of how infectious a disease can be.
Recovered population
On the table shown we can see how many people were not affected by the
black death or recovered from it. Eventhough it’s a significant amount the
other 1/3 of the entire population died.
Death people
There were approximately 40million people who died because of the disease,
Proving one more time how dangerous and lethal it is.
Quarantined People
The lack of efficient drugs and vaccines to treat the disease caused the
number of quarantined people to drop down significantly and sum up into
the continuous deaths from the infected.
Conclusions / Contributions
Policy making
Favor de aventarse CHORIZO
Findings after using the model
By reviewing the leverage points we found out that some of the variables
didn’t affect as much as we thought. Some other variables were pretty
obvious when affecting them and by using them we could realize how lethal
the black death was back on the years 1300-1400.