Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Lessons learned from implementation of a demonstration program to reduce the burden of anemia and hookworm in women in Yen Bai Province, Viet Nam

Background Iron deficiency, anemia and hookworm disease are important public health problems for women of reproductive age living in developing countries and affect the health of newborns and infants. Iron supplementation and deworming treatment are effective in addressing these problems in both pregnant and non-pregnant women. Daily iron supplementation and deworming after the first trimester is recommended for pregnant women although these programs usually do not operate efficiently or effectively. Weekly iron-folic acid supplementation and regular deworming for non-pregnant women may be a viable approach for improving iron status and preventing anemia during the reproductive years. Addressing these diseases at a population level before women become pregnant could significantly improve women's health before and during pregnancy, as well as their infants' growth and development. Methods and Results This paper describes the major processes undertaken in a demonstration intervention of preventive weekly iron-folic acid supplementation with regular deworming for all 52,000 women aged 15–45 years in two districts of Yen Bai province, in northern Viet Nam. The intervention strategy included extensive consultation with community leaders and village, commune, district and provincial health staff, and training for village health workers. Distribution of the drugs was integrated with the existing health service infrastructure and the village health workers were the direct point of contact with women. Iron-folic acid tablets and deworming treatment were provided free of charge from May 2006. An independent Vietnamese NGO was commissioned to evaluate compliance and identify potential problems. The program resulted in effective distribution of iron-folic acid tablets and deworming treatment to all villages in the target districts, with full or partial compliance of 85%. Conclusion Training for health staff, the strong commitment of all partners and the use of appropriate educational materials led to broad support for weekly iron-folic acid supplementation and high participation in the regular deworming days. In March 2008 the program was expanded to all districts in the province, a target population of approximately 250,000 WRA, and management was handed over to provincial authorities.