In the 1st lecture of the class, we discussed the role of the pancreas to control the output of the insulin for regulating blood glucose levels. When the pancreas does not produce enough insulin, glucose builds up resulting in Diabetes diseases. Today, diabetes has been risen to epidemic proportions, affecting about 8.5% of the total world adult population (according to the World Health Organization, WHO). A mathematical model that describes the total population size of diabetics is given below: dce +8+y+vC() + AND ANO-(+)CC) - AN(E) + (!) With initial condition Cit-0) - and Nit -0)-N, (0) C(C): Nt): Number of new cases of diabetes ie, the system input) Number of diabetics with complications The total number of diabetics with and without complications i... Probability of developing a complication Natural mortality rate Mortality rate due to complications Rate at which complications are cured Rate at which patients with complications become severely disabled V: Note that ... y. vare all constant. Assume the following values for parameters - y 0.02/year 0.05/year 0.08/year 0.05/year And the initial conditions are c-47,000 500 and N-61,100,500. Additionally, assume that the diabetic incident is constant I() -6x 10 2.) Compute the Laplace Transformation of the differential equations described above b.) Design a block diagram of the system showing the output N(S), the input (s), the transfer function and the initial conditions and N c.) Use any method to compute the analytic expression N(D) fort 0