Analysis The graph presented above demonstrates how the disease A H1N1 behaves during a 1000 day period considering the United States population at the time 2009 and the number of infected people at the start of the outbreak It illustrates that the Susceptible Population maintains steady until it starts to decrease while the Infected Population increases until approximately the day 500 and then starts to decrease The Infected Population increases greatly starting at the day 250 which also leads to the increase of the Recovered Population after the day 500 which is when the infected population starts to decrease In the Infected Population graph the maximum point translates to total or highest amount of people that will ever get infected and thus after it has reached the maximum point it starts to decrease The Infected Population starts to decrease because the population is starting to enter the recovery compartment This is due to the fact that there are measures being taken in order that the American population becomes healthy once again Some measures that were taken were by the Centers for Disease and Control Protection included 11 million regimens of antiviral drugs and personal protective equipment including over 39 million respiratory protection devices masks and respirators gowns gloves and face shields Centers for Disease and Control Protection 2010 The Recovery Population is mostly increasing since as a person stops being infected he she becomes a recovered person
There is never a decrease in the Recovery Population because once a person is infected their only outcomes are to recover or pass away The diseased population is considered as part of the recovered in the SIR Model because it is independent of population dynamics which include births deaths immigration emigration etc There are more complex models like the MSIR which takes into consideration maternally derived immunity the SEIR SEIS amongst others The H1N1 was a pandemic and because of this the susceptible population decreases as shown in the graph and they become infected and therefore enter the infected or recovered compartments The compartments are shown through a specific period of time t and the differential equations are used because the model is dynamic and therefore it means that the compartments change over time this change in time is continuous not discrete All the compartments are related when the infected population starts to decrease it puts a stop to the rise or fall of the susceptible population because the population starts to be recovered and therefore the number of infected individuals declines and since there are less individuals infected the chance of getting or transmitting the disease is lower as well Something that is demonstrated in the graph is that since the recovery rate of the Influenza is longer than most viruses the population recovers slower which ultimately means that the whole model is working more slowly than usually and thus to accurately represent the behavior a 1000 day period was crucial even though the original outbreak didn't last as long In the three graphs shown people move from susceptible to infected and then infected to recovered or diseased 2 Conclusion In conclusion the SIR model can be used to model an infectious disease as it is the H1N1 The H1N1 outbreak in the United States was extremely harmful and with the SIR model I could see how the disease behaved taking into consideration the data collected
Equally I had the opportunity to see for myself how doctors or public health workers research and estimate the behavior of the disease and because of that take the measures needed to provide the population with the necessary medication and vaccinations Through this extended essay I learned that the SIR model is in fact the simplest model and therefore does not take into consideration certain things that does influence the spread of the disease in a specific population This is the reason why the model has certain flaws The model I carried out ran for 1000 days because it was needed to mathematically represent the start and the decay of the sickness which couldn't have been made with a fewer amount of days Originally the H1N1 didn't last as long which demonstrates how the model was manipulated and flawed The enormous amount of people in the United States at the time also led the model to be inaccurate with the original data because the model can t control the circumstances in which a person gets infected i e it doesn't take into account the deaths and suggests that every person has the same chance of getting infected when in reality there are some who are more immune to the disease than others From the carrying out of this extended essay I realized how the SIR model can be used to predict the effects that the disease will have on the population Ultimately I learned how mathematics can be seen in every form including in the health department Public health workers can use this model to see how many supplies they are going to need to help the population recover Finally by modelling the H1N1 outbreak in the United States during 2009 I got to see how a disease can grow attack the population and then decay Using the SIR model also demonstrated how simple an infectious disease can be modelled in order to see how it affects a specific population which was in this case the United States population in 2009 Throughout this extended essay I got to see how two fields mathematics and health can come together to achieve an outcome that will be beneficial to both which was how a disease can be modelled and see the effects that it can on a population
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