Drug addiction is a widespread problem worldwide, inflicting substantial harm in terms of a large number of deaths and disability. Mostly people are recognizing it as a major public health challenge, and this awareness extends to both less developed and wealthier nations. This research introduced an innovative mathematical model, represented as \(S_D, E_D, H_D, L_D, R_D, C_D\) , to comprehensively explore the dynamics of drug addiction. The main goal is to analyze the extent of drug addiction in society. This involves considering two groups of individuals: those heavily addicted and those with a light addiction with rehabilitation. The model’s behavior has been examined through RK4 method conducted with Maple. We have been proposed the early identification and rehabilitation method as a control dynamic. This control strategy has been involved identifying drug users early on and providing treatment to minimize their influence on society and prevent them from becoming heavy drug addicts. Our simulations emphasize the pivotal role of interaction rates ( \(\gamma\) ) and rehabilitation rates ( \(\delta _1\) ) and ( \(\delta _2\) ) in controlling drug user population dynamics.
