Open AccessAnalysis of a mathematical model in the spread of tuberculosis epidemic with vaccination and relapse effect
Author(s) -
A N Ifati,
Sutimin Sutimin,
Ratna Herdiana,
Robertus Heri Soelistyo Utomo,
A. H. Permatasari
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1943/1/012131
Subject(s) - basic reproduction number , epidemic model , vaccination , tuberculosis , lyapunov function , transmission (telecommunications) , disease , medicine , mathematics , mathematical economics , virology , computer science , physics , environmental health , population , telecommunications , pathology , nonlinear system , quantum mechanics
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.