Diphtheria (a contagious bacterial disease) is spreading in a small village with a population size of 1000 inhabitants. Consider that the population is divided into three categories: susceptible, infected, and recovered (or removed). Once someone gets the infection this year, they cannot get the infection again. The village has a healthcare system that can facilitate vaccinations to prevent the spread of Diphtheria. The average length of the disease is 53 weeks, over which time the person is deemed infected and can spread the disease. The time period for the model is t = {0, 1, 2, ..., n}, number of weeks. Initially at t = 0, only 5 cases are reported. Given that a = 1/Tbar = 1/(average length of disease in weeks), and that after one week, the total number of the infected is 9, use the discrete SIR model to compute the value of r.