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

Abstract

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 (R0) that derived by next generation matrix. When the R0 less than one, NE state is stable. Then EE is stable if R0 exceed unity. The simulation result is presented to describe the dynamic of TB spread in a long time.