Optimizing Budget Allocation in an Integrated Water and Sanitation System Using Optimal Control Theory

More than 2.5 billion people lack access to an improved water supply and improved sanitation facilities. Most of them are from lower-income countries (LICs)—where annual municipal budgets for water and sanitation (WatSan) services are highly variable, often inadequate to cover current operation and maintenance, and difficult to use for investment in capital expansion projects. My research aims to provide a budget allocation system for municipal WatSan managers in LICs in the face of severe budget constraints; this budget allocation system aims to protect LICs from public health impacts associated with inadequate water and sanitation services. The process, called Sequential Budget Allocation, requires municipalities to set aside a portion of their annual budget for capacity expansion, and optimizes the allocation of these funds over the three services (drinking water supply—DWS, wastewater and sewage treatment—WST, and municipal solid waste management—MSW) and across the multiple service regions in the municipality. I first use a systems approach to construct an integrated water and sanitation system model (IWSS), which represents the deficit status of WatSan services in all regions. I use enteric diarrheal disease (EDD) as the indicator of impact of inadequate WatSan services. Then, I propose a nonlinear differential equations model called SIWDR (Susceptible-Infected-Water-Dumpsite-Recovered), which links the status of WatSan services to the total incidents of EDD in the service region. Finally, I use optimal control theory to allocate the budget to the three services across the multiple service regions in the municipality in a sequence of annual investments designed to minimize the incidence of EDD over a specified planning horizon. With certain budget constraints, the total cases of enteric diseases are minimized in SIWDR.