数学中国 Ww. madio. net 144 The UMAP Journal 29.2(2008) Retention of the model To quantify the efficiency ofa healthcare system, we consider how many iterations n of the healthcare process are required before Hn falls below some threshold Hinin. Hence, we substitute H,= Hnin into(1)and solve for n to find the retention R In Hmin In Ho+In(P+ AT-APT) The retention R measures how long the modeled system can operate, start- ing from a healthy population, before an overwhelming majority of the population is no longer healthy. A larger retention value indicates a more ifective system. For all calculations of R, we take Ho and Hmin to be 100 and I Economic Weighting One of the primary discriminatory factors of healthcare in the U.Sis economic status; we would Hke to take this into consideration. To do so we consider three economic dasses Group 1: Those who control the lowest quartile of wealth. Group 2: Those in the middle quartiles for wealth Group 3: Those in the upper quartile for wealth, We adjust the parameters A and T based on the wealth of a group Since our meta-metrics describe the average performance of the system our model-without the economic weightings presented in this section- describes the effect of the system on the average person, "a person of median wealth(hence in Group 2). Analogously, we treat the median per son in the lower quartile as a representative of Group I and the median person in the upper quartile as representative of Group 3 We adjust the probabilities A and T for Group 1 by a factor of C, the ratio of the median wealth of an individual in the lowest quartile to that of the average person. Since wealth in the U.S. is so unevenly distributed, comparing the me- dian individual in the upper quartile to the average person would be mis leading. Instead, we adjust the probabilities A and T for Group 3 by factor of C, which now represents the wealth of the median individual in the upper quartile with respect to the richest person in Group 3. This gives us a weight based on how the wealth is distributed in the upper quartile Simply put, these factors give us a sense of the economic disparity be tween the groups; quality of accessibly and treatment scales with wealth, and C and C, and appropriate scaling factors. We calculate their values in the Appendix数学中国ww.madio.net