Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Reducing the global burden of depression : population level analysis of intervention cost-effectiveness in 14 world regions

International evidence on the cost and effects of interventions for reducing the global burden of depression remain scarce. Aims: To estimate the population-level cost-effectiveness of evidence-based depression interventions and their contribution towards reducing current burden. Method: Primary-care-based depression interventions were modelled at the level of whole populations in 14 epidemiological subregions of the world. Total population-level costs (in international dollars or I$) and effectiveness (disability adjusted life years (DALYs) averted) were combined to form average and incremental cost-effectiveness ratios. Results: Evaluated interventions have the potential to reduce the current burden of depression by 10–30%. Pharmacotherapy with older antidepressant drugs, with or without proactive collaborative care, are currently more cost-effective strategies than those using newer antidepressants, particularly in lower-income subregions. Conclusions: Even in resource-poor regions, each DALYaverted by efficient depression treatments in primary care costs less than 1 year of average per capita income, making such interventions a cost-effective use of health resources. However, current levels of burden can only be reduced significantlyif there is a substantialincrease substantial increase intreatment coverage.

Correcting for bias when estimating the cost of hospital-acquired infection : an analysis of lower respiratory tract infections in non-surgical patients

Hospital acquired infections (HAI) are costly but many are avoidable. Evaluating prevention programmes requires data on their costs and benefits. Estimating the actual costs of HAI (a measure of the cost savings due to prevention) is difficult as HAI changes cost by extending patient length of stay, yet, length of stay is a major risk factor for HAI. This endogeneity bias can confound attempts to measure accurately the cost of HAI. We propose a two-stage instrumental variables estimation strategy that explicitly controls for the endogeneity between risk of HAI and length of stay. We find that a 10% reduction in ex ante risk of HAI results in an expected savings of £693 ($US 984).