The impact of the media awareness and optimal strategy on the prevalence of tuberculosis

摘要

In this present study, we propose and analyze a mathematical model of tuberculosis (TB) transmission considering social awareness effects during an epidemic. Possible equilibrium points of the model are investigated, and their stability criterion is discussed. Basic reproduction number R0 of the model is obtained through the next-generation matrix method. It has been shown that the infection-free equilibrium is locally stable when R0 < 1 and unstable for R0 > 1. The global asymptotic stability of the endemic equilibrium P* is verified by constructing a suitable Lyapunov function. The possibility of two endemic equilibria when R0 < 1 urges the system through backward bifurcation at R0=1 also verified using center manifold theory. The media awareness parameters influence the occurrence of backward bifurcation. An optimal control problem is framed considering a media intervention parameter u(t) as a control variable. The existence and characterization of the optimal solution to the problem solved analytically. Optimal media control strategy with accessible media intervention cost gradually reduce the prevalence of the disease. In addition to our analytical results, several numerical simulations are also performed to make the analysis more significant. A short discussion on the media guided transmission characteristic of the disease, obtained from our investigation is conducted at last.