Analyses of cataract surgery performed by the Unified Health System in Brazil, 2006-2007

Objective. Estimate cataract surgical rates (CSR) for Brazil and each federal unit in 2006 and 2007 based on the number of surgeries performed by the Unified Health System to help plan a comprehensive ophthalmology network in order to eliminate cataract blindness in compliance with the target set by the World Health Organization (WHO) of 3 000 cataract surgeries per million inhabitants per year. Methods. This descriptive study calculates CSR by using the number of cataract surgeries carried out by the Brazilian Unified Health System for each federal unit and estimates the need for cataract surgery in Brazil for 2006-2007, with official population data provided by the Brazilian Institute of Geography and Statistics. The number of cataract surgeries was compared with the WHO target. Results. To reach the WHO goal for eliminating age-related cataract blindness in Brazil, 560 312 cataract surgeries in 2006 and 568 006 surgeries in 2007 needed to be done. In 2006, 179 121 cataract surgeries were done by the Unified Health System, corresponding to a CSR of 959 per million population; in 2007, 223 317 were performed, with a CSR of 1 179. With the Brazilian Council of Ophthalmology estimation of 165 000 surgeries each year by the non-public services, the CSR for Brazil would be 1 842 for 2006 and 2 051 for 2007. The proportions needed to achieve the proposed target were 38.6% in 2006 and 31.6% in 2007. Conclusions. Human resources, technical expertise, and equipment are crucial to reach the WHO goal. Brazil has enough ophthalmologists but needs improved planning and infrastructure in order to eliminate the problem, aspects that require greater financial investment and stronger political commitment.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.