Global stability for a tuberculosis model
2011
Liu, Junli | Zhang, Tailei
A deterministic model is developed to describe the effects of vaccination and treatment on the spread of tuberculosis. It is shown that the basic reproduction number characterizes the disease transmission dynamics: if R₀≤1, there exists only the disease-free equilibrium which is globally asymptotically stable, and if R₀>1 then there is a disease endemic equilibrium and the disease persists. Global stability of the endemic equilibrium is also discussed. Analysis of the dependence of R₀ on the vaccination rate, vaccine efficacy and treatment rate shows that the spread of tuberculosis can be controlled if the vaccine rate or the efficacy or the treatment rate reaches a certain threshold.
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