The spread of a contagious disease through a population involves intricate interactions from the level of populations down to the level of individual cells and viruses. However, it is still possible to lean interesting and useful information from relatively simple models. The SIR model of an Epidemic ? Classic model introduced in 1927 ? Simple model that provide interesting and useful information ? Population divided in three groups: S ? Susceptible ? Infected Recovered R S (t) + I(t) + R(t) = 1 dS dt aSI dI dt - aSIBI dR dt = BI Proportion 1.0 0.8 Susceptible Recovered 0.6 0.4 0.2 Infected 0.0 0 10 20 30 40 하 Time (arb. units) 50 Figure 2: Temporal behavior of the proportion of individuals in each of the three compartments of the SIR model. This model is particularly relevant to a homogeneous population in an environment with little geographic distribution. A famous example of exactly this situation occurred in 1978 at a British boarding school. A single boy in the school of 763 students contracted the flu and it spread rapidly, as shown in the table below. t (days) I (students infected) 012345678201237 1 3 7 25 72 222 282 256 9 233 189 123 70 25 11 4 Assume that the parameter a = 1 66 in the SIR model for the data given. Using Excel, determine the value of ẞ such that the model matches the data.