JTAM (Jurnal Teori dan Aplikasi Matematika)
Vol 10, No 3 (2026): July

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

Nur Rahmi (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Wahyuni Ekasasmita (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Muhammad Rifki Nisardi (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Ahmad Fajri (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Muhammad Fadhil Nurahmad (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Hartina Husain (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie)
Ahmad Husain (Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie Department of Production and Industrial Technology, Institut Teknologi Bacharuddin Jusuf Habibie)



Article Info

Publish Date
24 Jun 2026

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.

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Journal Info

Abbrev

jtam

Publisher

Subject

Mathematics

Description

Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model ...