Mathematics Model SAHTR for the Number of Drug Abusers with Economic and Educational Factors

This study develops a mathematical model of drug abuse involving susceptible (S), light users (A), heavy users (H), treatment (T), and recovered (R) compartments, incorporating economic and educational factors. The analysis includes determining equilibrium points, assessing their stability, calculating the basic reproduction number, and performing numerical simulations using the Runge–Kutta Fehlberg method. Results show that the model yields two equilibrium points: drug-free and endemic. Both are stable when the inflow rate into the light-user compartment—affected by effective contact rate, anti-drug campaign effectiveness, and economic conditions—exceeds the outflow rate. Numerical simulations confirm the analytical findings and illustrate that reducing interactions between vulnerable individuals and drug users, strengthening anti-drug campaigns, and improving economic conditions can diminish the potential spread of drug abuse.