Studying the Fast or Slow Progression of the Primary Tuberculosis through Bifurcation and Global Sensitivity Analysis

Wenjing Zhang, Federico Frascoli, Jane Heffernan

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Mycobacterium tuberculosis infection can lead to<br>different disease outcomes: clearance, latent, and primary tuberculosis.<br>The primary tuberculosis is characterized by<br>fast or slow progression.<br>We analyzed a four dimensional with-in host tuberculosis infection model considering the interactions among macrophages, T lymphocytes, tuberculosis bacteria to reveal the determining<br>factors to the fast or slow active disease progression.<br>Mathematically, the slow progression occurs when<br>parameter values close to a single-zero bifurcation;<br>while the fast progression happens when parameter<br>values are far away from this bifurcation.<br>Global sensitivity analysis on the single-zero bifurcation conditions is performed on the<br>parameter values, which are significantly influence<br>the basic reproduction number.<br>The result shows the loss rate of infected macrophages is the most influential factor<br>to primary tuberculosis, followed by<br>cell-mediated immunity and infection rates.<br>Further bifurcation analysis on the infected<br>macrophages loss rate result the parameter ranges<br>for clearance, latency, and recurrent disease outcomes.<br>Global stability on the uninfected equilibrium<br>gives a sufficient condition for the complete<br>disease elimination.<br>Four coexisting infected equilibriums indicate<br>that clearance, latent, and active disease can be<br>determined by the initial infection dynamics.<br>All analytical results are confirmed by simulations.
Original languageEnglish
JournalMathematics in Applied Sciences and Engineering
StatePublished - 2020


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