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arXiv · 2604.15620

$PG-NODE^{TB}$: Physics-Guided Neural Ordinary Differential Equations for Tuberculosis Transmission Dynamics

Selain K. Kasereka·Eric M. Mafuta·Fadi Al Machot·Emmanuel M. Kabengele·Jean Chamberlain Chedjou·Kyandoghere Kyamakya
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Abstract

Tuberculosis (TB) remains a leading global infectious disease, causing approximately 1.3 million deaths and 10.6 million new infections annually. Classical compartmental ODE models are the standard epidemiological tool for TB, yet their fixed-parameter structure cannot adapt to time-varying dynamics, unmodeled effects, or heterogeneous real-world data. This paper presents a methodological framework and proof-of-concept for applying Physics-Guided Neural Ordinary Differential Equations (PG-NODE) to TB transmission modeling within a SLIR (Susceptible, Latent, Infectious, Recovered) compartmental framework. We perform a rigorous mathematical analysis of the SLIR model, including derivation of the basic reproduction number $\mathcal{R}_0$, equilibrium analysis, and normalized sensitivity indices. We then reformulate the SLIR system as a PG-NODE, preserving compartmental conservation laws and biological constraints while enabling neural network components to learn unknown or time-varying rate functions from data. Three simulation scenarios illustrate the framework's intended capabilities: (i) adaptive tracking of time-varying transmission rates, (ii) correcting for unmodeled treatment and relapse dynamics with 27\% lower RMSE than the classical SLIR, and (iii) comparative forecasting of competing intervention policies over a 20-year horizon. Simulation results indicate that PG-NODE has strong potential for improving predictive accuracy while maintaining epidemiological interpretability; full adjoint-based training on real WHO surveillance data is identified as the key next step for empirical validation.

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Selain K. Kasereka, Eric M. Mafuta, Fadi Al Machot, Emmanuel M. Kabengele, Jean Chamberlain Chedjou, Kyandoghere Kyamakya. 2026-04-17. $PG-NODE^{TB}$: Physics-Guided Neural Ordinary Differential Equations for Tuberculosis Transmission Dynamics. https://arxiv.org/abs/2604.15620

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