A structural Merton jump-diffusion framework for survival analysis: Modeling biological solvency and distance-to-death(DtD) in tuberculosis

Tuberculosis (TB) remains a leading cause of death globally, with early mortality often driven by severe malnutrition and human immuno-deficiency virus (HIV) co-infection. Traditional survival analyses identify risk factors but remain associative, failing to capture the dynamic physiological collapse preceding death. In a novel interdisciplinary adaptation, we applied the Merton jump-diffusion structural framework from quantitative finance to model survival as a state of biological solvency, in which mortality occurs when a stochastic health trajectory crosses a critical failure threshold. We analysed a retrospective cohort of 15,182 TB patients in Cameroon over two decades. Adjusted body mass index (BMI) was conceptualized as a proxy for health capital and modeled using a stochastic process accounting for individual recovery trends, physiological instability, and acute clinical shocks. The study included predominantly young adult males (median age: 33 years) with a median BMI of 20.7 kg/m2. HIV co-infection was present in 35% of patients. The overall mortality rate during the 240 days follow-up period was 7.0%, with 55.1% of deaths occurring within the first 30 days. The model identified a critical failure threshold at BMI 17.329 kg/m2. HIV co-infection emerged as a key driver of metabolic instability, significantly increasing physiological volatility. Statistical validation confirmed that sudden clinical shocks were necessary to explain observed mortality patterns. The resulting Distance-to-Death (DtD) metric slightly outperformed standard associative extended Cox models in predicting survival, achieving a higher discriminative ability in testing set (Harrells C-index: 0.781 vs. 0.772; p = 0.038). Patients stratified into the highest-risk category showed a mortality rate of 16.7%, compared with 1.6% in the most stable group.This study bridges financial engineering and clinical epidemiology, offering a mechanistic understanding of how physiological reserves and metabolic instability determine survival. To support clinical application, we developed an interactive digital triage tool enabling identification of high-risk patients in resource-limited settings. Author summaryTuberculosis remains a major cause of death worldwide, particularly in people with poor nutrition or co-infection with HIV. In this study, we explored a new way to understand why some patients survive while others do not. We adapted a method originally used in finance to track the "health reserves" of patients over time, using body weight and related measures to estimate how close someone is to a critical health threshold. Our approach captures both gradual health decline and sudden medical complications, such as severe infections or rapid deterioration. By applying this method to a large group of patients in Cameroon, we found that a very low body weight is a strong warning sign for impending death and that HIV infection makes health outcomes less predictable. We also created a simple scoring tool that can help doctors identify patients at greatest risk, so that life-saving interventions and closer monitoring can be prioritized. This work bridges mathematical modeling and clinical care, offering a new way to assess patient vulnerability and improve outcomes in resource-limited settings.