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Global analysis of a dynamical model for transmission of tuberculosis with a general contact rate

✍ Scribed by Samuel Bowong; Jean Jules Tewa

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
433 KB
Volume
15
Category
Article
ISSN
1007-5704

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✦ Synopsis

This paper deals with the global analysis of a dynamical model for the spread of tuberculosis with a general contact rate. The model exhibits the traditional threshold behavior. We prove that when the basic reproduction ratio is less than unity, then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable under certain conditions. The stability of equilibria is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the theoretical results.

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