Analyzing peak and late phase sensitivities in a delayed alcoholism model with Taylor wavelets

İmamoğlu Karabaş, Neslişah; Gümgüm, Sevin

doi:10.22124/jmm.2026.32955.2999

Analyzing peak and late phase sensitivities in a delayed alcoholism model with Taylor wavelets

Articles in Press

Document Type : Research Article

Authors

İzmir University of Economics

10.22124/jmm.2026.32955.2999

Abstract

We apply the Taylor wavelet collocation method to a nonlinear de-
layed SDTR alcoholism model and conduct a systematic sensitivity analysis that
reveals qualitatively different parameter roles at the epidemic peak and at the late
phase of the simulation. A fine sweep of the delay parameter τ uncovers a non-
monotonic response in every compartment, with an interior extremum that has not
been previously reported for this model class. Applying the method, continuous
piecewise-polynomial approximations of the model were obtained without lineariza-
tion. Accuracy of the method was confirmed through residual error calculations and
through a comparison with the MATLAB dde23 solver on the full simulation inter-
val. The method delivers continuous polynomial approximations on each subinterval
and reproduces benchmark DDE solutions on the full simulation horizon. Sensitiv-
ity analysis was performed at both epidemic peaks and at the late phase of the
simulation. It was found that parameters show significantly different behaviors over
these time scales. Social transmission has marked impacts on peak burden but re-
verses sign at the late phase. Treatment parameters show their largest sensitivities
at the late phase, with treatment-entry rate also acting strongly at the peak. Time
delay produces a non-monotonic effect—each compartment exhibits an interior ex-
tremum on the plausible range τ ∈ [0, 8], with Dpeak maximized near τ ≈ 2–3 and
D(t = 30) minimized near τ ≈ 4. These differences imply that controlling peaks
requires different intervention strategies than controlling late-phase addiction levels.

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