Effect of awareness programs in controlling the prevalence of an epidemic with time delay

Abstract

A nonlinear mathematical model with delay to capture the dynamics of effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware population. The model is analyzed using stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delay in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcation. © 2011 World Scientific Publishing Company.