State estimation for nonlinear state-space transmission models of tuberculosis

Area of Science:

• Epidemiology
• Mathematical Modeling
• Control Theory

Background:

• Tuberculosis (TB) presents a significant global health challenge with high mortality rates.
• Existing transmission models, like the Gammaitoni and Nucci (GN) model, rely on the quanta generation rate, which is not directly measurable.
• Accurate estimation of infectivity parameters is crucial for effective TB transmission control.

Purpose of the Study:

• To develop and validate state estimators for estimating the quanta generation rate from available measurements.
• To adapt the GN model into observable single-room and two-room configurations for estimation.
• To assess the performance of Kalman filters in estimating the quanta generation rate under different measurement scenarios.

Main Methods:

• Adaptation of the GN model into augmented single-room and simplified two-room models.
• Demonstration of model observability for theoretical estimation feasibility.
• Application of continuous-time extended Kalman filters (EKF) with a 60-second sampling rate.
• Utilization of a hybrid extended Kalman filter (HEKF) for a more realistic daily measurement sampling rate.

Main Results:

• Both adapted GN models were proven to be observable.
• The continuous-time EKF achieved accurate quanta generation rate estimates with a 60-second sampling rate.
• The HEKF successfully provided accurate quanta generation rate estimates with a daily sampling rate.

Conclusions:

• State estimators, particularly Kalman filters, can accurately estimate the unmeasurable quanta generation rate.
• The developed models and estimation techniques are viable for assessing TB transmission risk.
• Future applications may involve integrating these methods into control systems for real-time TB transmission reduction in confined settings like hospitals.