Bifurcation Analysis of Impact of Awareness Campaign on Alcoholism with Delay

Abstract

In this paper, transmission dynamics of alcoholism with media awareness programs has been studied by developing a mathematical model using delay differential equations. It is assumed that heavy alcohol drinking habit spreads by the direct contact between susceptibles and heavy alcohol consumers. The rate of growth of media awareness campaigns is assumed to be proportional to the number of deaths due to heavy alcohol drinking. We have formulated a compartmental model considering individual's behavioral changes due to the influences of awareness campaigns coverage and converted the unaware susceptible individuals into aware. Time delay factor is considered for the delay of conversion of unaware susceptible individuals into heavy alcoholic by their interaction. The stability analysis of equilibrium points is carried out. The basic reproduction number R₀ is computed by applying the next generation matrix approach. Moreover, sensitivity analysis of the parameters involved in R₀ is conducted employing normalized forward sensitivity technique. The model analysis revealed that the spread of alcoholism in the community can be controlled by awareness programs but it persists in the community as a drinking-present equilibrium. The drinking-present equilibrium exhibits Hopf bifurcation regarding time delay as the delay parameter. Numerical simulations provide the results of analytical outcomes and the significance of awareness campaigns and delay in mitigating alcoholism in society.