The analysis of a drug transmission model with family education and public health education

In this paper, we formulate a six dimensional drug transmission model to study the effect of family education and public health education. The dynamical behaviors of the model are discussed in terms of the basic reproduction number R0. By constructing Lyapunov functions, we obtain the drug-free equilibrium is globally asymptotically stable if R0≤1 and the drug addiction equilibrium is globally asymptotically stable if R0>1. Sensitivity analyses are performed to seek for effective control measures for drug spread. The analysis show that both the family and public health education can influence the spread of drug transmission. However, the combination of family and public health education is more effective to reduce the prevalence of drugs. Some numerical simulations are given to confirm the obtained theoretical results.