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<p>The Bayesian approach to sensitivity analysis and the numerical solution of inverse problems for a&#xa0;mathematical model of Tuberculosis (TB) prevalence in the Russian Federation based on a&#xa0;system of ordinary differential equations, taking into account both bacterioexcretion and without it. In the presence of incomplete and heterogeneous data, traditional point estimates of model parameters can lead to unreliable forecasts of expected incidence. To address this problem, a&#xa0;Bayesian approach is used to obtain posterior distributions of unknown epidemic parameters that take into account both prior knowledge and real data. The paper proposes epidemiologically prior distributions of unknown model parameters, taking into account literature data and point estimates for refining the model parameters using measurements of diagnosed individuals with and without bacterioexcretion over time intervals of up to 5 years. Using data from the Novosibirsk region as an example, it is shown that Bayesian confidence intervals for most epidemiological model parameters are robust to variations in prior distributions, with the exception of the passive detection rate. The obtained results and confidence intervals can be used to analyze the epidemiological situation and develop control measures in other regions of Russia.</p>

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Bayesian calibration and sensitivity analysis of ordinary differential equation models for Tuberculosis spread in the Russian Federation

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Olga Krivorotko,
  • Nikolay Zyatkov

摘要

The Bayesian approach to sensitivity analysis and the numerical solution of inverse problems for a mathematical model of Tuberculosis (TB) prevalence in the Russian Federation based on a system of ordinary differential equations, taking into account both bacterioexcretion and without it. In the presence of incomplete and heterogeneous data, traditional point estimates of model parameters can lead to unreliable forecasts of expected incidence. To address this problem, a Bayesian approach is used to obtain posterior distributions of unknown epidemic parameters that take into account both prior knowledge and real data. The paper proposes epidemiologically prior distributions of unknown model parameters, taking into account literature data and point estimates for refining the model parameters using measurements of diagnosed individuals with and without bacterioexcretion over time intervals of up to 5 years. Using data from the Novosibirsk region as an example, it is shown that Bayesian confidence intervals for most epidemiological model parameters are robust to variations in prior distributions, with the exception of the passive detection rate. The obtained results and confidence intervals can be used to analyze the epidemiological situation and develop control measures in other regions of Russia.