TB-SEIRZ-Q: Modeling the epidemiology tuberculosis in Russia with multidrug resistance and quarantine

The purpose of the research is to develop and systemically analyze a comprehensive mathematical model of tuberculosis epidemiology in Russia, taking into account multidrug resistance (MDR-TB) and quarantine measures, to formalize the dynamics of infection and provide information support for management decisions.

Methods. The methodology of systems analysis was used. A deterministic mathematical model (TB-SEIRZ-Q) described by a system of nonlinear ordinary differential equations was developed. The model expands classical approaches by introducing a latent stage, stratification of infected people by sensitivity to treatment and bacterial excretion, as well as separate quarantine groups. An analysis of the stability of the model was carried out, the basic reproductive number (R₀) was calculated using the next-generation method. The parameters were identified based on official data for Russia. Numerical modeling of the epidemic dynamics and sensitivity analysis of key parameters were performed.

Results. The TB-SEIRZ-Q model was obtained that adequately describes the specifics of TB. The estimated basic reproduction number R₀ ≈ 2,258, indicating instability of the disease-free state and the transition of the system to endemic equilibrium. The results of numerical modeling demonstrate high correspondence to the real data on TB incidence in Russia for 2018-2023 (R² = 0,92). Sensitivity analysis revealed the key role of infection transmission and isolation rates in the R0 value. Increasing the isolation efficiency to 0,5 reduces R₀ below 1 (to 0,95), providing the possibility of eliminating the epidemic.

Conclusion. The developed TB-SEIRZ-Q model is an effective tool for systemic analysis of the tuberculosis epidemic in Russia. It formalizes the infection dynamics taking into account MDR-TB and quarantine measures, as well as an information basis for assessing and optimizing epidemic management strategies. The model allows predicting the development of the situation and quantifying the impact of various interventions, such as strengthening quarantine measures.

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