Analysis of a Heroin Epidemic Model with Saturated Treatment Function

Table 1

Description of variables and parameters of model (1).

Variable	Description
	Number of susceptible individuals at time
	Number of heroin users who have been successfully treated from heroin use, as well as individuals who have voluntarily stopped using the heroin (and have withdrawal symptoms) “self-cure" at time
	Number of heroin users undergoing treatment at time
	Number of drug users not undergoing treatment at time , that is, the initial and relapsed heroin users
	Total population at time ()
Parameter	Description
	Recruitment rate of individuals in the general population entering the susceptible population
	Effective contact rate
	Death rate due to natural causes
	Rate at which individuals undergoing treatment relapse to heroin use
	“Self-cure rate": rate at which heroin users stop using heroin and join the successfully cured class of individuals not taking heroin
	Heroin-related death rate of heroin users not in treatment
	Heroin-related death rate of individuals undergoing treatment
	Rate at which heroin users in treatment are successfully cured (i.e., completely detoxicated) from heroin use
	Rate at which heroin users are treated
	The extent of saturation of heroin users within the community