A Mathematical Model of Wasting–Stunting Dynamics with Age-Dependent Nutritional Recovery in Children under Five

Nur Rahmi; Wahyuni Ekasasmita; Muhammad Rifki Nisardi; Ahmad Fajri; Muhammad Fadhil Nurahmad; Hartina Husain; Ahmad Husain

doi:10.31764/jtam.v10i3.39083

A Mathematical Model of Wasting–Stunting Dynamics with Age-Dependent Nutritional Recovery in Children under Five

Nur Rahmi, Wahyuni Ekasasmita, Muhammad Rifki Nisardi, Ahmad Fajri, Muhammad Fadhil Nurahmad, Hartina Husain, Ahmad Husain

Abstract

Childhood wasting and stunting remain major public health challenges, yet their long-term interaction at the population level remains insufficiently understood. This study develops a deterministic compartmental model to investigate wasting–stunting dynamics among children under five years of age in Indonesia by classifying the population into four nutritional states: well-nourished, moderately wasted, severely wasted, and stunted. An important feature of the model is the incorporation of age-dependent recovery weighting based on infant population proportion, allowing recovery rates to differ between infants and older children according to demographic composition. Model parameters are estimated using nonlinear least-squares calibration based on aggregated national prevalence data from Indonesia during 2013–2024. Concurrent wasting–stunting is incorporated implicitly within the stunting dynamics to maintain model parsimony. The analysis includes threshold, local stability, and normalized sensitivity analyses. The calibrated model produced a residual error of approximately 8.77×〖10〗^(-3), indicating good agreement with observed prevalence data. Numerical simulations show declining and stabilizing behavior for severe wasting, whereas stunting remains persistent over time. Threshold analysis indicates that the condition R_W<1 is associated with decay of wasting dynamics and convergence toward equilibrium. Sensitivity analysis indicates that deterioration and progression toward stunting dominate long-term dynamics, while infant-related recovery parameters exhibit relatively low sensitivity rankings. These findings suggest that reducing wasting alone may not substantially lower stunting prevalence and highlight the importance of integrated interventions targeting both acute and chronic undernutrition pathways.

Keywords

Age-dependent Recovery; Child Malnutrition; Stunting-wasting; Stability Analysis; Sensitivity Analysis.

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DOI: https://doi.org/10.31764/jtam.v10i3.39083