Optimal control strategy for the effects of hard water consumption on kidney-related diseases

Abstract

Objectives: We study the optimal control strategy for the effects of hard water consumption on kidney-related diseases. The mathematical model has been formulated and studied to gain insights on the optimal control strategy on the effects of hard-water consumption on kidney-related diseases. The positivity and boundedness of the solutions are determined. A global sensitivity analysis has been performed and the numerical solutions have been carried out. Results: A global sensitivity analysis shows that the control on water is an important parameter. This can reduce the proportion of individuals with kidney-dysfunction and hence reduces the proportion of individuals with kidney-related diseases. Furthermore, the numerical solutions show that with the optimal control, the proportion of individuals with kidney-related diseases can be minimised.