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.