This paper proposes and analyzes a mathematical model of tuberculosis and HIV co-infection that specifies for Russian Federation regions, based on mass balance law and described by eight ordinary differential equations. A sensitivity-based identifiability analysis of this mathematical model was performed, which revealed the sensitivity of the averaged parameters of the models to statistical real data of infectious individuals based on the Sobol method. The problem of identifying the sensitive epidemiological parameters (contagiousness, the rate of tuberculosis activation, additional mortality rate, etc.) for the model was reduced to the problem of minimization of the quadratic misfit function. The numerical results of the modeling of the number of people expected to be infected with tuberculosis and HIV were shown and discussed for the Sverdlovsk and Moscow regions of the Russian Federation. It has been shown that increasing the capacity of the medical system by 10% will make it possible to reduce the number of diagnosed cases of active tuberculosis by 2 times over the next 3 years in some 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.

Understanding the heterogeneous spread of tuberculosis (TB), particularly multidrug-resistant (MDR) forms and the role of subclinical infection, is critical for achieving the WHO End TB strategy. This study develops a novel compartmental model that explicitly incorporates incipient and subclinical TB together with MDR forms, and links them to case detection and treatment pathways. The key innovation lies in integrating a sensitivity-based identifiability analysis with a Bayesian MCMC framework to quantify parameter uncertainty and correlations directly from regional surveillance data. Applied to five high-burden regions of the Russian Federation (2009–2020), the approach reveals strong heterogeneity in epidemic drivers: wide credible intervals for contagiousness, the rate of progression to bacterio-positive (BE+) states, and detection rates. The probabilistic forecasts up to 2025 are validated against 2021–2023 data. The region-specific differences in these correlated parameters dictate transmission dynamics, and improving detection of BE+ cases is the most effective lever for control.