Sensitivity, Bifurcation, and Stochastic Analysis of Tuberculosis Progression

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steadystate transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Further, bifurcation analysis unfolds various disease outcomes induced by the variation of macrophage apoptosis rate, which depend on the number of bacteria engulfed and released by macrophages. We then develop an Itˆo SDE model, which considers demographic variations at the cellular level to study stochastic fluctuations at the cellular level.

References:

1. Zhang, Wenjing, et al. ”An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis.” Journal of mathematical biology 83.3 (2021): 1-32.
2. Zhang, Wenjing. ”Deterministic and stochastic in-host tuberculosis models for bacteriumdirected and host-directed therapy combination.” Mathematical Medicine and Biology: A Journal of the IMA 39.2 (2022): 126-155