Dynamics of synthetic drugs transmission model with psychological addicts and general incidence rate

Synthetic drugs are replacing traditional ones and becoming the main popular ones gradually, which have given rise to serious social issues in recent years. In this paper, a synthetic drugs transmission model with psychological addicts and general contact rate is proposed. The local and global stabilities are decided by the basic reproduction number R0. By analyzing the sensitivity of parameters, we obtain that controlling psychological addiction is better than drugs treatment. These results are verified by numerical simulations.