Exploring the Fucntion of the SIR Model

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Infectious diseases had major impacts and influences in the human history. Diseases such as Spanish Influenza or the Bubonic Plague have remarkable positions in history. Disease spread models are used to predict outcomes of an epidemic. These models are used to calculate the impact of an infectious disease, funding required for mass vaccinations and data for public health departments. The earliest mathematical model of infectious diseases was created by Daniel Bernoulli in 1766. This model was used to predict the outcome of inoculation against smallpox disease. In the modern world, these models are created using various software programs. The reason why I chose this subject is because I previously worked on some modelling simulations. Also my father is in the healthcare sector, so this topic looked very exciting to me. Predicting outcomes of infectious epidemics may save thousands of lives and millions of dollars. In the healthcare sector, accuracy and reliability is very important. In this project, the work function of the SIR epidemic model and some of its derivatives will be explored along with some theorems about this models. SIR model is the fundamental model of almost all modern epidemic models. SIR model is the most widely used disease spread model in the world. Also it is a simple epidemic model which has mathematics that commensurate with our class.
SIR Model
The model is created by W.O. Kermack and A.G. McKendrick in 1927. SIR Model has three compartments: Susceptible, infected and removed.
S: denotes the number of individuals who are not infected with the disease. These people are vulnerable to catch the disease.
I: represents the number of individuals who have been infected. These people can transfer the disease to pe...

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...we use one of these three models for Malaria the predictions would be incorrect. Malaria cannot be transmitted with air or water, it is either transmitted by mosquitos or by blood from an infective individual. The main mathematical concept behind the SIR models are differential equations. The graphs are created by computer programs that uses mathematical algorithms. The last model I explained is the most accurate model in all those three models. However it also have missing points, for example the mortality rate of disease is not included but it is a very important parameter. To improve SIR Model and its successors, help from doctors and health specialists are needed. Creating an epidemic model requires a synergy between programmers, mathematicians and health professionals. Nevertheless, creating an accurate model requires financial support and hard-working experts.

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