10. A simple model of infectious disease spread is U' = VW-mu-pu V' = qv- mv-rvw W' = rvW -mw- vw 46 Modeling, Change, and Simulation where v, m, p, q, and r are positive constants. The variables U, V, and W stand for susceptible population, infected (but not symptomatic) population, and symptomatic population (but not in that order). a) Which variable represents which population? Justify your answer. b) How would you model 1. a "safe-contact" program that reduced the probability of infection per encounter? 2. a drug that slowed the progression from infection to the appearance of symp- toms (as AZT did for HIV / AIDS)? 3. a drug that cures the disease, in the sense that it makes infected people fully recovered but not immune