Mathematical modeling of refugee population dynamics and its impact on deforestation in Tanzania: An ODE-based and neural network-enhanced approach

Abstract

Understanding the interplay between refugee population dynamics and environmental factors is crucial for sustainable policy planning and public health preparedness. This study integrates an ordinary differential equation (ODE)-based model with a Neural Network-Enhanced Approach to estimate key parameters governing these interactions. A system of differential equations models refugee settlement, land-use changes, and deforestation, while Physics-Informed Neural Networks (PINNs) refine parameter estimates by minimizing discrepancies between observed and predicted states. Results show that combining traditional ODE modeling with neural networks improves predictive accuracy, capturing nonlinear interactions more effectively than regression-based methods. Specifically, the study examines bifurcation behavior concerning the refugee influx rate ($\mu$), deforestation rate ($\beta$), and reforestation effort coefficient ($\gamma$). The analysis reveals that all three distributions are unimodal, peaking around 0.10 for $\alpha$, 0.12 for $\beta$, and 0.08 for $\gamma$, with positive skewness indicating longer tails towards higher values. These findings underscore the urgent need for policy interventions to curb deforestation while enhancing reforestation efforts. Importantly, environmental degradation and rapid population pressures identified in the model have direct implications for public health, including increased risk of waterborne and vector-borne diseases, reduced access to clean air and food sources, and long-term mental and physical health challenges for displaced populations. Overall, this study highlights key environmental impact drivers and their health consequences, emphasizing the necessity of integrated, cross-sectoral planning in refugee-hosting regions.