Bifurcation analysis of a tuberculosis progression model for drug target identification

Abstract

Tuberculosis (TB) is a major cause of morbidity and mortality worldwide. The emergence and rapid spread of drug-resistant M. tuberculosis strains urge us to develop novel treatments. Experimental assays are restricted by lab capacity, insufficient funds, low numbers of laboratory animals and obsolete technology. Systems-level approaches to quantitatively study TB can overcome these limitations. Previously, we proposed a mathematical model describing the key regulatory mechanisms underlying the pathological progression of TB. Here, we systematically explore the effect of parameter variations on disease outcome. We find five bifurcation parameters that steer the clinical outcome of TB: number of bacteria phagocytized per macrophage, macrophages death, macrophage killing by bacteria, macrophage recruitment, and phagocytosis of bacteria. The corresponding bifurcation diagrams show all-or-nothing dose-response curves with parameter regions mapping onto bacterial clearance, persistent infection, or history-dependent clearance or infection. Importantly, pathogenic stage strongly affects the host’s sensitivity to these parameter variations. We identify parameter values corresponding to a latent-infection model of TB, where disease progression occurs significantly slower than in progressive TB. Two-dimensional bifurcation analyses uncovered synergistic parameter pairs which could act as efficient compound therapeutic approaches. Through bifurcation analysis, we reveal how modulating specific regulatory mechanisms could steer the clinical outcome of TB.