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Abstract <p>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.</p>

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Stationary Analysis of a Disease Coinfection Model: Tuberculosis and HIV in Regions of Russia

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. V. Neverov,
  • O. I. Krivorotko,
  • G. D. Kaminskii

摘要

Abstract

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.