Journal
JOURNAL OF BIOLOGICAL DYNAMICS
Volume 13, Issue 1, Pages 26-42Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2018.1563218
Keywords
Effective contact rate; vaccination; tuberculosis; basic reproduction number; global stability
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Funding
- Women for Africa Foundation
- Diputacion Foral de Bizkaia and Deustotech-Deusto Foundation
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The long and binding treatment of tuberculosis (TB) at least 6-8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infectious disease caused by the bacillus Mycobacterium tuberculosis. Adults are principally attacked. In this work, we assess the impact of vaccination in the spread of TB via a deterministic epidemic model (SV ELI) (Susceptible, Vaccinated, Early latent, Late latent, Infectious). Using the Lyapunov-Lasalle method, we analyse the stability of epidemic system (SV ELI) around the equilibriums (disease-free and endemic). The global asymptotic stability of the unique endemic equilibrium whenever is proved, where is the reproduction number. We prove also that when is less than 1, TB can be eradicated. Numerical simulations, using some TB data found in the literature in relation with Cameroon, are conducted to approve analytic results, and to show that vaccination coverage is not sufficient to control TB, effective contact rate has a high impact in the spread of TB.
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