Table 1 The description of parameters of the \(\mathbb{SMA}\) model (1.2)

π

Recruitment rate of susceptible individuals

0.5

Assumed

μ

Natural death rate

0.05

[48]

β

Transmission rate of addiction to the susceptible individuals

0.1–0.8

[48]

σ

Contact rate of susceptible individuals with addicted individuals

0.2

[48]

α

Proportion of exposed individuals that join addicted class

0.7

[48]

ρ

Induce death rate

0.01

Assumed

δ

Individuals that leave exposed class

0.25

[48]

ϵ

Addicted individuals that join recovered class due to the treatment

0.7

[49]

κ

Susceptible individuals that don’t use and/or quit from using \(\mathbb{SM}\)

0.01

Assumed

γ

Proportion of recovered individuals susceptible to \(\mathbb{SMA}\)

0.35

[50]

η

Individuals that leave recoverd class

0.4

[49]