Development of a sustainable water resource financing mathematical model for donors and end-users

Rural villages and underdeveloped communities represent the largest group challenged by poor water supply and sanitation with inequalities in resources to adequately implement potential solutions and even more with their high risk level of financing, funding is particularly challenging for water projects. Innovative financing alone will not eliminate the burdens of rural villages and underdeveloped communities. The purpose of this thesis is to address the lack of sustainable water financing of water projects in rural areas using a novel framework of a mathematical model based on "system dynamics" using optimal feedback control theory to maximize the performance of a water project. This is achieved by using feedback loops that allow for a real-time adjustment of the input parameters. The case model presented considers a renewable water supply system for a rural village where the user's willingness to pay along with demand drive the performance indicators to simulate how decision makers can make real-time decisions on how to manage financing instruments and long-term debt. The results of the study are the first step to the mathematical framework of optimal control of cash flows. Future research is aimed at applying optimal control using ordinary differential equations and stochastic differential equations which is presented in theoretical form.