Analysis of an epidemic model with awareness programs by media

Abstract

The purpose of this study is to investigate the effects of awareness programs by media on the epidemic outbreak and controlling on the diseases. Also, in this study a non-linear mathematical model for the effects of awareness programs on the spread of infectious diseases for example flu has been proposed and analyzed. In the modeling process it is assumed that disease spreads because of the contact between susceptibles and infectives. The increase rate of awareness programs impacting the population is assumed to be relative to the number of infective individuals. It is further assumed that because of the effect of media, susceptible individuals form a divide class and avoid contact with the infectives. We analyzed the model by finding the feasibility and the stability of the equilibrium points by using the Routh-Hurwitz criteria and also using the direction and stability of Hopf bifurcation. The model analysis shows that the spread of an infectious disease can be controlled by using awareness programs but the disease remains endemic because of immigration. Numerical examples are used to show the stability of the equilibrium point