The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems

Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian-based representations of reaction-diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based "auxiliary regions". We demonstrate that the hybrid method is able to simulate reaction-diffusion dynamics for a number of different test problems with high accuracy. Further, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including, filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table

Rapid urban malaria appraisal (RUMA) I: Epidemiology of urban malaria in Ouagadougou

BACKGROUND: Rapid urbanization in sub-Saharan Africa has a major impact on malaria epidemiology. While much is known about malaria in rural areas in Burkina Faso, the urban situation is less well understood. METHODS: An assessment of urban malaria was carried out in Ouagadougou in November -December, 2002 during which a rapid urban malaria appraisal (RUMA) was applied. RESULTS: The school parasitaemia prevalence was relatively high (48.3%) at the cold and dry season 2002. Routine malaria statistics indicated that seasonality of malaria transmission was marked. In the health facilities, the number of clinical cases diminished quickly at the start of the cold and dry season and the prevalence of parasitaemia detected in febrile and non-febrile cases was 21.1% and 22.0%, respectively. The health facilities were likely to overestimate the malaria incidence and the age-specific fractions of malaria-attributable fevers were low (0–0.13). Peak prevalence tended to occur in older children (aged 6–15 years). Mapping of Anopheles sp. breeding sites indicated a gradient of endemicity between the urban centre and the periphery of Ouagadougou. A remarkable link was found between urban agriculture activities, seasonal availability of water supply and the occurrence of malaria infections in this semi-arid area. The study also demonstrated that the usage of insecticide-treated nets and the education level of family caretakers played a key role in reducing malaria infection rates. CONCLUSION: These findings show that determining local endemicity and the rate of clinical malaria cases are urgently required in order to target control activities and avoid over-treatment with antimalarials. The case management needs to be tailored to the level of the prevailing endemicity

Preventing childhood malaria in Africa by protecting adults from mosquitoes with insecticide-treated nets

Malaria prevention in Africa merits particular attention as the world strives toward a better life for the poorest. Insecticide-treated nets (ITNs) represent a practical means to prevent malaria in Africa, so scaling up coverage to at least 80% of young children and pregnant women by 2010 is integral to the Millennium Development Goals (MDG). Targeting individual protection to vulnerable groups is an accepted priority, but community-level impacts of broader population coverage are largely ignored even though they may be just as important. We therefore estimated coverage thresholds for entire populations at which individual- and community-level protection are equivalent, representing rational targets for ITN coverage beyond vulnerable groups