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### P24 - Simple approaches for demographic estimations during health projective studies

Background — In the early nineteen century, the growth of human population occupies the mind of some mathematicians like Verhulst and Quetelet (~1844). According to Quetelet, for an uninhibited growth at former stages, the population increase rate is proportional to the size of population, so that

dP = rP (1),

dt

where r is the intrinsic Malthusian parameter. As soon as obstacles appear, an inhibiting component, proportional to –P2 , takes place in (1), that is to say

dP = rP - b P2 (2).

dt

This was the assumption of Verhulst to find a curve that would describe this contextual condition, recovered later by R. Pearl and L. Reed (1920).

Aims — To propose a pragmatic model to project population growth for more accurate treatment of health data.

Methods — The concept of carrying capacity K was applied. We took it above all as a measure of the urban sanitation state and work market saturation translated to inhabitants load tha t the city environment supports. We explained the essential relation between exponential growth and geometric progression. An integro-differential approach, formulated by the author, was adopted to compute non-local features that interfere with population growth. Proposed equation is

dP = P (0) ((1+r)t in (1+r) – 1/24 & #8747;1/ & #8731;r & #773;dr) (3), with

dt

intrinsic Malthusian parameter r in logistic evolution. The last census (2000) of IBGE — Instituto Brasileiro de Geografia — was assumed as a premise of calculus.

Results — The study reveled good approximations with the real increasing of Brazilian population. The mean difference between model projection and IBGE projection for 2004 was –2.72%. The model was utilized to project population for next 16 years without adjustments in carrying capacity.

Conclusions — This simple model was developed in R language and demonstrates great utility alied to TabWin, the well-known free tabulator disseminated by Health Ministry. We wait this article calls attention to the necessary and prudent adjustments of health data to a realistic population growth. We are not suggesting that IBGE’s projecting model is misguided. Rather we wait for mutual cooperation and comprehension about the practical needs of final users (physicians, health professionals, studants, etc.).