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Table 2 Parameter values and ranges obtained from data fitting

From: Modelling the trends of inpatient and outpatient rehabilitation for methamphetamine in the Western Cape province of South Africa

  Description Range Value Source
\(\beta\) The effective contact rate between users and susceptibles 0.10–0.21 \(0.105\, \mathrm{year}^{-1}\) [15]
\(\eta\) The relative ability for outpatients to initiate new users 0–0.0099 \(0.009612\, \mathrm{year}^{-1}\) Estimated
p Proportion of users recruited into inpatient rehab 0–1 \(0.352~\mathrm{year}^{-1}\) Estimated
\(\varepsilon\) The effectiveness of rehab 0–1 \(0.6080\, \mathrm{year}^{-1}\) Estimated
\(\sigma\) The rate at which users are recruited into rehab 0–0.05024 \(0.02827\, \mathrm{year}^{-1}\) Estimated
\(\delta _0\) The rate of quitting abuse for outpatients 0.001–1 \(0.01\, \mathrm{year}^{-1}\) Estimated
\(\delta _1\) The rate of quitting abuse for inpatients 0.01–1 \(0.3142~\mathrm{year}^{-1}\) Estimated
\(\rho _1\) Relapse rate for outpatients 0–0.054 \(0.0382\, \mathrm{year}^{-1}\) Estimated
\(\rho _2\) Relapse rate for inpatients 0–0.0235 \(0.0020\, \mathrm{year}^{-1}\) Estimated
\(\gamma _1\) Transfer rate from outpatient rehab to inpatient rehab 0–0.06012 \(0.02961\, \mathrm{year}^{-1}\) Estimated
\(\gamma _2\) Transfer rate from inpatient rehab to outpatient rehab 0–0.008 \(0.003\, \mathrm{year}^{-1}\) Estimated
\(\Pi\) Recruitment rate into the susceptible population 0.028–0.080 \(0.04\, \mathrm{year}^{-1}\) [15]
\(\mu\) Natural death rate 0.019–0.021 \(0.020\, \mathrm{year}^{-1}\) [41]
  1. MA methamphetamine