We intend to design a system for optimal control (u₁(t), u2(t)) which represent the Tuberculosis (TB) treatment rates for latent class and infectious class, respectively. Our target is to minimize the TB infected individuals (including latent and infectious individuals) as well as the costs required to con- trol TB by treating latent and infectious individuals, over a certain time horizon [0,tf]. The cost of each intervention is assumed to be proportional to the square of its intensity. Thus we formulate the optimization problem below. Minimize the objective function ' A₁E(t) + A₂I(t) + ¹¹³u²(t) + Bu²(t) J(u(.)), u(·) = "h 1 subject to dS = A(1p) BSI+ kV - ds, dt dV dt dE ུ|ཙ⪜ཊྛི|༴ཁྱི|ཙ dt dt = Ap-kV - dV, = BSI - (u(t) ++ d)E + OR, dR = E-(d--u2(t))I, = u₁(t)Eu(t) (d+ 0)R S(0) = So≥0, V(0) = √≥0, E(0) = Eo ≥0,1(0) = 10 ≥0, R(0) = Ro≥ 0. The control variables are assumed to be bounded: Given any t > 0, 0

What is the significance of R and R2 in gression model?

Assume that a population of patients contains 30% of individuals who suffer from a certain fatal syndrome Z, which simultaneously makes it uncomfortable for them to take a life-prolonging drug X. Let Z = 1 and Z = 0 represent, respectively, the presence and absence of the syndrome, Y = 1 and Y = 0 represent death and survival, respectively, and X = 1 and X = 0 represent taking and not taking the drug. Assume that patients not carrying the syndrome, Z = 0, die with probability 0.5 if they take the drug and with probability 0.5 if they do not. Patients carrying the syndrome, Z = 1, on the other hand, die with probability 0.7 if they do not take the drug and with probability 0.3 if they do take the drug. Further, patients having the syndrome are more likely to avoid the drug, with probabilities p(X = 1|Z=0) = 0.9 and P(X = 1|Z = 1) = 0.6 . Based on this model, compute the joint distributions and  for all values of x, y, and z. Present the following joint distributions in tables. [Hint:…

A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • X2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables 1 if advanced 3o if not if aeroderivative 3o if not X3 = and x4 = Write the model equation for advanced engine type.