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.

We propose an algorithm for modeling scenarios for newly diagnosed cases of COVID-19 in the Republic of Kazakhstan. The algorithm is based on treating incomplete epidemiological data and solving the inverse problem of reconstructing the parameters of the agent-based model (ABM) using the set of available epidemiological data. The main tool for constructing the ABM is the Covasim open library. In the event of a drastic change in the situation (appearance of a new strain, removal or introduction of restrictive measures, etc.), the model parameters are updated taking into account additional information for the previous month (online data assimilation). The inverse problem is solved by stochastic global optimization (of tree-structured Parzen estimators). As an example, we give two scenarios of COVID-19 propagation calculated on December 12, 2021 for the period up to January 20, 2022. The scenario that took into account the New Year holidays (published on December 12, 2021 on http://covid19-modeling.ru ) almost coincided with what happened in reality (the error was 0.2%).

Steady-state (stationary) solutions to a system of four nonlinear ordinary differential equations are found, analyzed, and used in mathematical epidemiology to describe long-term infections. Stability conditions for stationary solutions are obtained in a model of coinfection of two diseases one of which is treatable. It is proved that a stationary endemic state (sluggish epidemic) of two simultaneous infections is stable within its permissible range. Heterogeneity in the stability (instability) of a nontrivial stationary state across regions of Russia is established using the example of tuberculosis and HIV coinfection. It is also shown that in regions where the nontrivial stationary state is unstable (regions on the way to tuberculosis elimination), the time until elimination ranges from 13.6 to 25.5 years.

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.

This paper investigates the identifiability of a spatial mathematical model of the spread of fast-moving epidemics based on the law of acting masses and diffusion processes. The research algorithm is based on global methods of Sobol sensitivity analysis and Bayesian approach, which together allowed to reduce the variation boundaries of unknown parameters for further solving the problem of parameter identification by measurements of the number of detected cases, critical and dead. It is shown that for identification of diffusion coefficients responsible for the rate of movement of individuals in space, it is necessary to use additional information about the process.