Speakers
Description
A novel mathematical model is developed that links the tuberculosis (TB) care cascade with the dynamics of healthcare worker adherence. The model extends standard TB compartmental frameworks by incorporating a health-worker supervision parameter and an evolutionary game for adherence to treatment protocols. We derive an analytic expression for the basic reproduction number $R_0(z)$ as a function of supervision intensity $z$, and we prove conditions for disease invasion and stability. In particular, we show that health-worker supervision alters the epidemic threshold and can induce a backward bifurcation: even if $R_0 < 1$, a stable endemic equilibrium may persist under weak supervision. We obtain an explicit inequality for backward bifurcation involving the cascade and relapse parameters. Combining behavioural and epidemiological thresholds, we identify a composite control criterion ($z > \max\{zc, ze\}$) that guarantees disease elimination. Numerical simulations (bifurcation diagrams and time-series) validate the analysis and illustrate how increasing z drives the system to a disease-free equilibrium. Our results highlight how implementation fidelity fundamentally changes TB transmission dynamics and provide quantitative guidance for achieving elimination.
