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Zbl 1217.34082
Huo, Hai-Feng; Dang, Shuai-Jun; Li, Yu-Ning
Stability of a two-strain tuberculosis model with general contact rate. (English)
[J] Abstr. Appl. Anal. 2010, Article ID 293747, 31 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

Summary: A two-strain tuberculosis model with general contact rate which allows tuberculosis patients with the drug-sensitive Mycobacterium tuberculosis strain to be treated is presented. The model includes both drug-sensitive and drug-resistant strains. A detailed qualitative analysis about positivity, boundedness, existence, uniqueness and global stability of the equilibria of this model is carried out. Analytical results of the model show that the quantities $R_1$ and $R_2$, which represent the basic reproduction numbers of the sensitive and resistant strains, respectively, provide threshold conditions which determine the competitive outcomes of the two strains. Numerical simulations are also conducted to confirm and extend the analytic results.

MSC 2000:: *34C60 Applications of qualitative theory of ODE
92D30 Epidemiology
34D20 Lyapunov stability of ODE
34D05 Asymptotic stability of ODE
34C28 Other types of "recurrent" solutions of ODE
92C50 Medical appl. of mathematical biology

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Zentralblatt MATH Berlin [Germany]