The mathematical modelling of the dual system of tuberculosis control in the USSR: a mathematical analysis of the infectious process.

Abstract

The tuberculosis (TB) epidemic in the Soviet and post-Soviet space represents a unique case in global epidemiology, shaped by the long-term interaction between coercive state structures, distorted surveillance systems, and inherited scientific paradigms. This article develops a mathematical framework for analyzing the dual system of TB control in the USSR—one that simultaneously generated conditions for sustained transmission within carceral institutions while publicly promoting a narrative of eradication. The study integrates historical epidemiology, structural analysis of Soviet penal institutions, and a review of mathematical models of TB and HIV/AIDS to construct a dual-population model incorporating totalitarian fragmentation, differential visibility of disease, and the asymmetric relationship between civilian and incarcerated populations. The article critically assesses limitations of classical compartmental models when applied to the post-Soviet TB context, emphasizing the cumulative effects of unreliable surveillance data, ideological distortions in diagnostic systems, and the inability of phthiriasis paradigms to account for structural determinants of infection. Employing elements of the morphological concept of epidemic diffusion, the proposed model reconstructs key mechanisms underlying epidemic persistence, including reinfection loops, suppression of epidemiological knowledge, and the emergence of a stable pathological equilibrium sustained by political–institutional dynamics. Mathematical analysis demonstrates the existence of a totalitarian fragmentation threshold beyond which TB becomes self-reinforcing, even under conditions of partial policy intervention. The model further explains why conventional elimination strategies fail in settings where penal systems act as chronic infectious reservoirs and where epidemiological visibility is systematically reduced. The findings underscore the necessity of incorporating institutional structures, knowledge asymmetries, and political constraints into models of infectious disease in the post-Soviet region. This study provides a theoretical foundation for future empirical research and offers a methodological framework for analyzing epidemics in environments characterized by data scarcity, institutional opacity, and structural violence.