A mathematical model of a heroin epidemic: Implications for control policies

Abstract

An exponential model based on the infectious disease model of Kermack and McKendrick has been simplified to illustrate how the use of heroin spreads in epidemic fashion. A numerical simulation is arranged to show how the dynamics of spread are influenced by the original number of users, rates of conversion, and time of removal from the drug scene of those secondarily affected. The spread is significantly increased by small increases of those originally affected, in which case reduction of spread requires a large increase in rate of removal. The model indicates a strategy for intervention which is discussed in relation to policies for control of drug abuse.