Mathematical Modeling to Prioritize Water Interventions in - PowerPoint PPT Presentation

Using Survey Data and Mathematical Modeling to Prioritize Water Interventions in Developing Countries Jane Cox, Konnor Petersen, and Jordan Spencer Dr. Tyler Jarvis https://math.byu.edu/waterdata

Changing Charity with Data • Maximize impact • Optimize resources being used • Locate underserved areas Photo by dii9c from Pexels

Water Interventions Tested • Chlorine Distribution • Dug Wells • Drilled Wells • Standpipes

Model Breakdown Reduced Travel & Years Gained Im Improved Health __________________ ___________________ = Cost Capital Costs & Operational Maintenance

Data Source • Survey participants are assigned to clusters • Cluster GPS Data is connected to the 15-20 surveys • Individual location not given due to privacy laws.

Cluster Boundaries: Voronoi Diagramming • Needed to know where survey participants were located • Consistent and logical way to divide the region

Estimating Household Locations • Need survey participant location to calculate time saved when a new water source is introduced • Individual Geographical information is not provided due to privacy laws

Household Sampling for Urban Clusters • Households are assumed to be distributed uniformly across cluster • Optimal well is placed after households to calculate new time spent gathering water

Household Sampling for Rural Clusters • Sampling is repeated and time saved is averaged • Number of population centers is random and uniformly distributed

Gamma Distribution α (shape) and β (scale) are calculated using the mean and variance of given survey data

Model Breakdown Reduced Travel & Years Gained Im Improved Health __________________ ___________________ = Cost Capital Costs & Operational Maintenance

Results: Namibia

Results: Angola

Sensitivity Analysis • Derivatives of estimated variables were checked • Results were positive, variables with high sensitivity are reasonable

Changing Charity with Data • Maximize impact • Optimize resources being used • Locate underserved areas Photo by dii9c from Pexels

Future Research: • Water table data in more accurately determining optimal intervention • Expand model to easily accommodate more countries • Utilize in real world application