Asymptotic Analysis and Identifiability in Dynamical Models for Water Resource Allocation in Kenya

Water resource allocation in Kenya is a complex dynamical system influenced by seasonal rainfall variability and human intervention. We developed a mathematical model incorporating climatic and socio-economic data, applied asymptotic analysis techniques, and conducted sensitivity tests on parameter identifiability. Our model demonstrates that the annual rainfall proportion significantly impacts water availability across different regions of Kenya. Sensitivity analysis revealed critical parameters affecting water resource distribution. The developed models provide a robust framework for understanding water resource dynamics in Kenya, facilitating more effective management strategies. Policy-makers should consider climate variability when planning future water resources allocations and investments. Water Resource Allocation, Dynamical Systems, Asymptotic Analysis, Identifiability The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.