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Epidemic-guided deep learning for spatiotemporal forecasting of Tuberculosis outbreak

Madhab Barman, Madhurima Panja, Nachiketa Mishra, Tanujit Chakraborty

TL;DR

This work tackles TB spatiotemporal forecasting by integrating a mechanistic MN-SIR epidemic model with graph-based diffusion into deep learning forecasters. Two architectures, EGDL-Parallel and EGDL-Series, fuse epidemiological signals with data-driven learning, supported by Bayesian parameter estimation and global stability analysis. Across Japan and China TB datasets, the EGDL framework achieves robust short- to medium-term forecasts, provides uncertainty quantification via conformal prediction, and offers explainability through temporal Grad-CAM and block-wise analysis. The approach demonstrates generalizability across regions with different mobility patterns and highlights practical utility for guiding region-specific public health interventions, while outlining avenues for incorporating richer mobility data and covariates in future work.

Abstract

Tuberculosis (TB) remains a formidable global health challenge, driven by complex spatiotemporal transmission dynamics and influenced by factors such as population mobility and behavioral changes. We propose an Epidemic-Guided Deep Learning (EGDL) approach that fuses mechanistic epidemiological principles with advanced deep learning techniques to enhance early warning systems and intervention strategies for TB outbreaks. Our framework is built upon a modified networked Susceptible-Infectious-Recovered (MN-SIR) model augmented with a saturated incidence rate and graph Laplacian diffusion, capturing both long-term transmission dynamics and region-specific population mobility patterns. Compartmental model parameters are rigorously estimated using Bayesian inference via the Markov Chain Monte Carlo approach. Theoretical analysis leveraging the comparison principle and Green's formula establishes global stability properties of the disease-free and endemic equilibria. Building on these epidemiological insights, we design two forecasting architectures, EGDL-Parallel and EGDL-Series, that integrate the mechanistic outputs of the MN-SIR model within deep neural networks. This integration mitigates the overfitting risks commonly encountered in data-driven methods and filters out noise inherent in surveillance data, resulting in reliable forecasts of real-world epidemic trends. Experiments conducted on TB incidence data from 47 prefectures in Japan and 31 provinces in mainland China demonstrate that our approach delivers robust and accurate predictions across multiple time horizons (short to medium-term forecasts), supporting its generalizability across regions with different population dynamics.

Epidemic-guided deep learning for spatiotemporal forecasting of Tuberculosis outbreak

TL;DR

This work tackles TB spatiotemporal forecasting by integrating a mechanistic MN-SIR epidemic model with graph-based diffusion into deep learning forecasters. Two architectures, EGDL-Parallel and EGDL-Series, fuse epidemiological signals with data-driven learning, supported by Bayesian parameter estimation and global stability analysis. Across Japan and China TB datasets, the EGDL framework achieves robust short- to medium-term forecasts, provides uncertainty quantification via conformal prediction, and offers explainability through temporal Grad-CAM and block-wise analysis. The approach demonstrates generalizability across regions with different mobility patterns and highlights practical utility for guiding region-specific public health interventions, while outlining avenues for incorporating richer mobility data and covariates in future work.

Abstract

Tuberculosis (TB) remains a formidable global health challenge, driven by complex spatiotemporal transmission dynamics and influenced by factors such as population mobility and behavioral changes. We propose an Epidemic-Guided Deep Learning (EGDL) approach that fuses mechanistic epidemiological principles with advanced deep learning techniques to enhance early warning systems and intervention strategies for TB outbreaks. Our framework is built upon a modified networked Susceptible-Infectious-Recovered (MN-SIR) model augmented with a saturated incidence rate and graph Laplacian diffusion, capturing both long-term transmission dynamics and region-specific population mobility patterns. Compartmental model parameters are rigorously estimated using Bayesian inference via the Markov Chain Monte Carlo approach. Theoretical analysis leveraging the comparison principle and Green's formula establishes global stability properties of the disease-free and endemic equilibria. Building on these epidemiological insights, we design two forecasting architectures, EGDL-Parallel and EGDL-Series, that integrate the mechanistic outputs of the MN-SIR model within deep neural networks. This integration mitigates the overfitting risks commonly encountered in data-driven methods and filters out noise inherent in surveillance data, resulting in reliable forecasts of real-world epidemic trends. Experiments conducted on TB incidence data from 47 prefectures in Japan and 31 provinces in mainland China demonstrate that our approach delivers robust and accurate predictions across multiple time horizons (short to medium-term forecasts), supporting its generalizability across regions with different population dynamics.

Paper Structure

This paper contains 35 sections, 2 theorems, 79 equations, 15 figures, 9 tables, 1 algorithm.

Key Result

Theorem 1

The disease-free equilibrium $(S_0, 0)$ of the model Eq. submodel is globally asymptotically stable when the basic reproduction number is less than 1 ($\mathcal{R}_0 < 1$).

Figures (15)

  • Figure 1: (A) Geographic distribution of Japan's 47 prefectures, shown for illustrative purposes only, without implying any political assertions on Japan's territorial boundaries. (B) Monthly active tuberculosis (TB) cases were recorded in each of Japan's 47 prefectures from January 1998 to December 2015.
  • Figure 2: (A) Geographic distribution of 31 provinces of mainland China, shown for illustrative purposes only, without implying any political assertions on China's territorial boundaries. (B) Log-transformed values of monthly active tuberculosis (TB) cases recorded in each of China's 31 provinces from January 2014 to December 2018 (log transformation is applied only for visual clarity).
  • Figure 3: Epidemic-Guided Deep Learning (EGDL). The upper panel of the plot represents a schematic architecture of the modified networked SIR (MN-SIR) model, and the lower panel showcases the workflow of the EGDL-Parallel framework (left) and the EGDL-Series approach (right). The demonstration is given using Japan's TB dataset.
  • Figure 4: (A) The Laplacian matrix corresponding to the network depicted in Fig. \ref{['fig:TB47']}(A), representing the connectivity and structure of the nodes in the system. This matrix captures the relationships between neighboring nodes and is essential for analyzing diffusion processes and other network dynamics. (B) Pairwise correlation of TB incidence cases recorded at 47 prefectures of Japan.
  • Figure 5: (A) The Laplacian matrix corresponding to the network depicted in Fig. \ref{['Fig_China_MAP']}(A), representing the connectivity and structure of the nodes in the system. This matrix captures the relationships between neighboring provinces in mainland China and is essential for analyzing diffusion processes and other network dynamics. (B) Pairwise correlation of TB incidence cases recorded at 31 provinces of mainland China.
  • ...and 10 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2