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Global stability for a tuberculosis model

โœ Scribed by Junli Liu; Tailei Zhang

Book ID
104047219
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
248 KB
Volume
54
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

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 R 0 โ‰ค 1, there exists only the disease-free equilibrium which is globally asymptotically stable, and if R 0 > 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 R 0 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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