Reaction-diffusion mechanisms explain the limited survival benefit of high-dose rifampicin in tuberculous meningitis

Clinical trials show that high-dose rifampicin markedly increases central nervous system (CNS) exposure in tuberculous meningitis without improving survival. To explain this discrepancy, we develop a coupled reaction--diffusion--pharmacokinetic/pharmacodynamic (PK/PD) model integrating spatial dynamics of \textit{Mycobacterium tuberculosis}, rifampicin transport across the blood--CNS interface, immune activation with steroid-induced suppression, and drug-induced hepatotoxicity. A threshold function governing the stability of the disease-free equilibrium is derived and analyzed through linear stability theory, numerical simulations, and sensitivity methods. Under both standard- and high-dose regimens, simulations show diffusion-driven smoothing of bacterial heterogeneity and convergence to a common disease-free attractor. Sensitivity and identifiability analyses indicate that outcomes are governed by reaction-dominated mechanisms, chiefly intrinsic bacterial killing and immune modulation. In a global sensitivity analysis, the influence of transport parameters on mortality is statistically indistinguishable from zero. The operative mechanism is pharmacodynamic saturation: the standard dose already attains $95.7\%$ of the maximal bactericidal effect, so a $3.5$-fold dose increase adds only $3.0$ percentage points and displaces the stability threshold by $4.4\%$. The model also reproduces the exposure--hepatotoxicity trade-off without a survival gain. Therapeutic progress is therefore more likely to come from enhancing intrinsic bactericidal activity or optimizing immune modulation than from further dose escalation.