We obtain a Lie algebra admitted by the system of equilibrium equations for nematocholesteric, which models configurations elastic field in one-constant approximation continuum theory. In case pure nematic, is found to admit ten-dimensional algebra, while cholesteric, admits four-dimensional algebra. addition, we have received particular analytical solutions model equations.

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...