Backward bifurcation in a mathematical model for tuberculosis with loss of immunity
Abstract
A mathematical model is developed to study the impact of loss of immunity on the transmission dynamics of tuberculosis (TB). Center manifold theory is applied to show that a backward bifurcation may occur under certain conditions, that is, a stable endemic steady-state may exist for R0 < 1. For a simplified model, it is shown that the unique endemic equilibrium is locally asymptotically stable if R 0 > 1. Sensitivity and uncertainty analysis using Latin Hypercube Sampling (LHS) method are presented to evaluate the variability of the model outcomes as a result of alternating parameter values, and to determine which parameters play key roles in producing the observed variability. Stochastic simulations are also performed.
Degree
Ph.D.
Advisors
Feng, Purdue University.
Subject Area
Mathematics|Biology|Biostatistics|Statistics|Public health
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