Question

3. A hospital trauma unit has determined that 25% of its patients are ambulatory and 75% are bedridden at the time of arrival at the hospital. A month after arrival, 65% of the ambulatory patients have recovered, 15% remain ambulatory, and 20% have become bedridden. After the same amount of time, 15% of the bedridden patients have recovered, 25% have become ambulatory, 50% remain bedridden, and 10% have died. Determine the percentages of patients who have recovered, are ambulatory, are bedridden, and have died 1 month after arrival. By using a matrix form for this discrete dynamical system, determine the eventual percentages of patients of each type of patient. (Hint: consider the closed formula for each type of patient based on the eigenvalues of the matrix and compute the limit when t > 0).

Answer 1

Answer:

EDACAC Jelsage four © Here, the patient can be in trenee States. recoverd, ambulatory, bedridden and dead. So, Initial probability vector is :- 0 NOW, Transition matriz is, are PE 0.25 0.75 M- 0.65 0 15 یا وہ 0025 0.2 0.5 01 - Here, note that once recoverd, patient stays in that state and also, once dead, patient remains dead

the percentages of Here now, After a month, we get patients in each state by 02275 Mo p = 0.225 0425 0.075 which here clearly tells that, 27.54% patients recoverd 22-54 patients Ambulatory 42.5% patients bedridden 7.5% patients dead Answer

I hope you understood my answer. Please give Up vote(LIKE) my answer. Thank you......