Mathematical modeling on the effects of drug abuse to the societies

Abstract

Drug abuse remains to be the global burden causing a large number of death and disability, it is now termed as a significant threat to public health for both developed and developing coun tries. This work presents a mathematical model as a new approach towards understanding and controlling the drug abuse in Tanzania. The mathematical model to study the effect of drug abuse in the society is developed and analyzed in this study. The model’s transmission process is considered as a social contact process between susceptible individuals and drug users based on the epidemiology principles. The model used the factors that were identified through feasi bility study as the significant factors that control the dynamics of drug abused population in the particular society. The model is analyzed using next generation matrix method the numberof new drug users that one drug user can produce in the entire period of abuse is computed and identifies as an epidemic threshold value, R0. Using R0 the condition for existence and stabil ity of stationary point is established. Using numerical simulation, the dynamical behavior of the model is explored and the result shows the significant contribution by the rate of adequate contact between the susceptible individual and the drug user, and the rate of recovery of drug user after rehabilitation as the major factors or players that dictate the dynamics of drug user population in the society. The model is finally analyzed to study the dynamical behavior of the drug abuse when control is applied, the result shows the drug users are minimized significantly. The result signifiesthe importance of early control of the drug abuse problem through establish ment of the strict laws that will narrow the possibility of this bad practice in societies. It is then vividly justified that, key result arising from this model is that prevention is indeed better than cure.