Bayesian Analysis of Tuberculosis Spread Scenarios in Regions of Russian Federation

The paper proposes a new model of Tuberculosis (TB) dynamics taking into account multi-drug resistant forms, which takes into account the detection of infected people with and without bacterial excretion. The model is described by a system of nine nonlinear ordinary differential equations united by the law of mass action and controlled by 10 epidemiological parameters. The conditions for the stability of the system’s equilibrium states are obtained, and the sensitivity-based identifiability analysis of the model is conducted using the Sobol method. Based on Bayesian optimization, the boundaries of sensitive parameters are specified and posterior distributions of the model parameters are obtained for five regions of the Russian Federation based on statistics from 2009 to 2020. It is shown the heterogeneity of epidemic situation by wide credible intervals of correlated parameters of virus contagiousness, the proportion of infected TB converting to the bacterial excretion form and the rate of detection of TB infected with bacterial excretion. Probabilistic forecasts of the expected number of TB infections to 2025 are constructed and validated to the 2021-2023 data.