An Optimal Control Framework to Address the Relationship between Water Resource Management and Water-Borne Health Impacts: Focus on the Texas Lower Rio Grande Valley

The objective of this study is develop a theoretical model that can evaluate two types of public health expenditures on water-borne health risks: water-related municipal services, an ex ante preventative measure against water-borne contamination, and medical treatment, an ex post treatment of the water-borne pollutant’s harmful effects on human health. The modeled community can allocate resources in either centralized-municipal water-services, point-of-use water-services, or medical intervention, with expenditures subject to a budget constraint. The movement of a water-borne illness through the community is modeled with a susceptible-infected-susceptible (SIS) disease framework. An optimization framework is developed, including a statement of the problem’s Hamiltonian and first-order-conditions. The first-order-conditions are discussed. Future work includes obtaining a numerical solution to the optimization problem.