Analysis of a mathematical model in the spread of tuberculosis epidemic with vaccination and relapse effect

Tuberculosis (TB) is a contagious disease that still exists in a community. A mathematical model incorporating vaccinated treatment and the effect of relapse of the disease is studied. This research is modified with vaccinated to reduce the rate of transmission and relapse condition in a healing per...

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Bibliographic Details
Published in:Journal of physics. Conference series 2021-07, Vol.1943 (1), p.12131
Main Authors: Ifati, A N, Sutimin, Herdiana, R, Utomo, R H S, Permatasari, A H
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematical models
Tuberculosis
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Summary:Tuberculosis (TB) is a contagious disease that still exists in a community. A mathematical model incorporating vaccinated treatment and the effect of relapse of the disease is studied. This research is modified with vaccinated to reduce the rate of transmission and relapse condition in a healing period. The model is analysed to verify the dynamical behaviour of the equilibriums. The nonendemic equilibrium (NE) state is determined by Castillo-Chaves theorem for the stability of global and the endemic equilibrium (EE) state using Lyapunov method. The existence of EE is determined by reproductive number (ℛ 0 ) that derived by next generation matrix. When the ℛ 0 less than one, NE state is stable. Then EE is stable if ℛ 0 exceed unity. The simulation result is presented to describe the dynamic of TB spread in a long time.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1943/1/012131