Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling

In this paper, we propose and analyze a mathematical model describing the effect of awareness programs by public media on the prevalence of Typhoid fever. A threshold quantity $R_{0}$, similar to the basic reproduction number is derived. We investigate the biologically meaningful equilibrium points and their local stability analysis. The global stability analysis has been performed with respect to the disease free equilibrium (DFE) $E_{0}$ by considering suitable Lyapunov function. We derive the stability condition of the DFE point $E_{0}$ and the interior steady-state $E^{*}$ with respect to the basic reproduction number $R_{0}$. We perform the analysis of Hopf-bifurcation with respect to the rate of executing awareness programs which has a substantial role on the dynamics of the model system. We investigate extensive numerical simulations to validate our analytical findings.