Caldwell2019 - The Vicodin abuse problem

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Short description
This is a mathematical model of Vicodin use and abuse used to investigate methods of combating Vicodin abuse in a population of patients who have obtained the drug through prescription. Mathematical descriptions of transitions through acute, chronic, abusive, and in-treatment populations are included.
Related Publication
  • The Vicodin abuse problem: A mathematical approach.
  • Caldwell WK, Freedman B, Settles L, Thomas MM, Camacho ET, Wirkus S
  • Journal of theoretical biology , 12/ 2019 , Volume 483 , pages: 110003 , PubMed ID: 31513802
  • School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States; X Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM, United States. Electronic address:
  • The prescription drug epidemic in the United States has gained attention in recent years. Vicodin, along with its generic version, is the country's mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. The majority of Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else's. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers.
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

hasProperty (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

Curation status


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Model files

Caldwell2019.xml SBML L2V4 Representation of Caldwell2019 - The Vicodin abuse problem 37.90 KB Preview | Download

Additional files

Caldwell2019.cps COPASI file of Caldwell2019 - The Vicodin abuse problem 66.83 KB Preview | Download
Caldwell2019.sedml SED-ML file of Caldwell2019 - The Vicodin abuse problem 3.68 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Oct 29, 2019 2:00:11 PM
  • Last Modified: Oct 29, 2019 2:00:11 PM
  • Version: 2 public model Download this version
    • Submitted on: Oct 29, 2019 2:00:11 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000840
: Variable used inside SBML models

Species Initial Concentration/Amount

3.76E7 item

700000.0 item

2000000.0 item

5640000.0 item

3760000.0 item
Reactions Rate Parameters
M => compartment*alpha_2*M alpha_2 = 0.45
T => A compartment*gamma_3*A*T gamma_3 = 8.0E-10
=> M; A compartment*lambda/(1+rho*A) rho = 1.0E-6; lambda = 3000000.0
M => C1 compartment*alpha_1*M alpha_1 = 0.22
C1 => C2 compartment*delta*C1 delta = 0.05
C2 => A compartment*delta*C2 delta = 0.05
Curator's comment:
(added: 29 Oct 2019, 13:59:44, updated: 29 Oct 2019, 13:59:44)
Reproduced plot of Figure 3 in the original publication. Model simulated and plot produced using COPASI 4.24 (Build 197).