数学中国 Ww. madio. net Better Living through Math 143 Definition of the model Let A, T, and P be the countrys accessibility, treatment, and prevention meta-metrics, We treat them as probabilities of certain events occurring within the healthcare system P: the probability that an individual will be in good health; A: the probability that an individual win have access to affordable health care, should they need it; and T: the probability that a sick individual will be correctly diagnosed and properly treated. We model a healthcare system as the stochastic process pictured in Fig- ure 1, and we repeatedly apply this process to track the flow of healthy individuals through the system. Healthy Success 99 Figure L Model of the healtheare process, with four states and probabilities of transitions among If at some time n we have a population of H, healthy individuals, then weexpect Hn (1- P)of those people to fall into poor health in the next time interval. Of those who fall ill, a proportion AT of them will find access to treatment and become healthy. Hence, we predict the number of healthy individuals after n+ l units of time to be Hx+I= H,-H(1-P)+H,(1-P)AT. For an initial healthy population Ho, this simplifies to Hn=H0(P+AT-APT)”数学中国ww.madio.net