In this paper, we proposed and analyzed the mathematical model of methamphetamine epidemics with the role of family was taken into account. The objective of this research was to investigate the role of family on the transmission model of methamphetamine epidemics. The standard method of differential equations was used to analyze the proposed model, to find the drug free equilibrium points and drug present equilibrium point of the model and to determine the stability of the proposed model for both equilibrium points. The drug reproductive number (R0 ) was found by applying the next generation matrix. The analytic solution and numerical solution were carried out. The results shown the proposed model which represented by five differential equations, consist of five subgroups that were the susceptible, light methamphetamine users, hard methamphetamine users, clients of health services in treatment and recovered individuals. We found that there were two equilibrium points, drug free equilibrium point and drug present equilibrium point. From the numerical simulation, when the effective of the role of family k = 0.9, the drug reproductive number R0 = 0.4928 <1, which mean that the methamphetamine epidemic was not occurred. Whenever the effective of the role of family k = 0.1, the drug reproductive number R0 = 0.37296 >1 which mean that the methamphetamine epidemic was occurred. Both drug free equilibrium points and drug present equilibrium points were local asymptotically stable. We concluded that if we increase the effective of the role of family (k) in the human population, then the methamphetamine users will decrease

Naowarat_2018_J._Phys. _Conf._Ser._1039_012036