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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.15620 |
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| _version_ | 1866908973397966848 |
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| author | Kasereka, Selain K. Mafuta, Eric M. Machot, Fadi Al Kabengele, Emmanuel M. Chedjou, Jean Chamberlain Kyamakya, Kyandoghere |
| author_facet | Kasereka, Selain K. Mafuta, Eric M. Machot, Fadi Al Kabengele, Emmanuel M. Chedjou, Jean Chamberlain Kyamakya, Kyandoghere |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15620 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $PG-NODE^{TB}$: Physics-Guided Neural Ordinary Differential Equations for Tuberculosis Transmission Dynamics Kasereka, Selain K. Mafuta, Eric M. Machot, Fadi Al Kabengele, Emmanuel M. Chedjou, Jean Chamberlain Kyamakya, Kyandoghere Dynamical Systems Optimization and Control 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. |
| title | $PG-NODE^{TB}$: Physics-Guided Neural Ordinary Differential Equations for Tuberculosis Transmission Dynamics |
| topic | Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2604.15620 |