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Table 5 Asymptotic analysis of the ODE solutions. The last column indicates the time needed until all participants become former smokers. This will never happen for HE participants, where less than 27% of them can ever become former smokers

From: Effectiveness of motivational interviewing, health education and brief advice in a population of smokers who are not ready to quit

  Eigenvalues (λ1, λ2, λ3) Equilibrium (U, I, M, F) Average Prevalence (U(t), I(t), M(t), F(t)) Time (years)
BA (−0.9, − 6353.3, − 0.7) (0, 0, 0, 100) (6.734, 4.96, 9.798, 78.508) 11.878
MI (−63.68, −0.17, −110.36) (0, 0, 0, 100) (6.293, 4.526, 4.246, 84.935) 40.664
HE (−1.743, −1.17, 0) (73.31, 0, 0, 26.68) (66.762, 5.252, 3.608, 24.378) Infinity
  1. Notes: MI, HE and BA are the abbreviations for Motivational Interviewing, Health Education and Brief Advice, respectively. For HE group 8.445 years is needed to reach that equilibrium. The notations U, I, Mand F represent the prevalence of indecisive, motivated, unmotivated and former smokers at the equilibrium, respectively