PubMed · 5014259
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1972-03-25. Doctors and overpopulation.. https://pubmed.ncbi.nlm.nih.gov/5014259/
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BACKGROUND: Meta-analyses of randomized controlled trials suggest that elective induction of labour at 41 weeks' gestation, compared with expectant management with selective labour induction, is associated with fewer perinatal deaths and no increase in the cesarean section rate. The authors studied the changes over time in the rates of labour induction in post-term pregnancies in Canada and examined the effects on the rates of stillbirth and cesarean section. METHODS: Changes in the proportion of total births at 41 weeks' and at 42 or more weeks' gestation, and in the rate of stillbirths at 41 or more weeks' (versus 40 weeks') gestation in Canada between 1980 and 1995 were determined using data from Statistics Canada. Changes in the rates of labour induction and cesarean section were determined using data from hospital and provincial sources. RESULTS: There was a marked increase in the proportion of births at 41 weeks' gestation (from 11.9% in 1980 to 16.3% in 1995) and a marked decrease in the proportion at 42 or more weeks (from 7.1% in 1980 to 2.9% in 1995). The rate of stillbirths among deliveries at 41 or more weeks' gestation decreased significantly, from 2.8 per 1000 total births in 1980 to 0.9 per 1000 total births in 1995 (p < 0.001). The stillbirth rate also decreased significantly among births at 40 weeks' gestation, from 1.8 per 1000 total births in 1980 to 1.1 per 1000 total births in 1995 (p < 0.001). The magnitude of the decrease in the stillbirth rate at 41 or more weeks' gestation was greater than that at 40 weeks' gestation (p < 0.001). All hospital and provincial sources of data indicated that the rate of labour induction increased significantly between 1980 and 1995 among women delivering at 41 or more weeks' gestation. The associated changes in rates of cesarean section were variable. INTERPRETATION: Between 1980 and 1995 clinical practice for the management of post-term pregnancy changed in Canada. The increased rate of labour induction at 41 or more weeks' gestation may have contributed to the decreased stillbirth rate but it had no convincing influence either way on the cesarean section rate.
We formulate schemes for the numerical solution of size-dependent population models. Such schemes discretize size by means of a natural grid, which introduces a discrete dynamics. The schemes are analysed and optimal rates of convergence are derived. Some numerical experiments are also reported to demonstrate the predicted accuracy of the schemes.