## Caldwell2019 - The Vicodin abuse problem

Model Identifier
BIOMD0000000840
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.
Format
SBML (L2V4)
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: wendy.caldwell@asu.edu.
• 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.
Contributors
Johannes Meyer

hasProperty
Mathematical Modelling Ontology Ordinary differential equation model

Curation status
Curated

Modelling approach(es)

Tags
Name Description Size Actions

### Model files

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

Caldwell2019.sedml SED-ML file of Caldwell2019 - The Vicodin abuse problem 3.68 KB Preview | Download
Caldwell2019.cps COPASI file of Caldwell2019 - The Vicodin abuse problem 66.83 KB Preview | Download
• Model originally submitted by : Johannes Meyer
• Submitted: Oct 29, 2019 2:00:11 PM
##### Revisions
• Version: 2
• Submitted on: Oct 29, 2019 2:00:11 PM
• Submitted by: Johannes Meyer
• With comment: Automatically added model identifier BIOMD0000000840
Legends
: Variable used inside SBML models

Species
Species Initial Concentration/Amount
M

C14140
3.76E7 item
C1

C14141
5640000.0 item
C2

C14141
3760000.0 item
A

C16522
2000000.0 item
T

treatment
700000.0 item
Reactions
Reactions Rate Parameters
(M) => (C1)

([C14140]) => ([C14141])
compartment*alpha_1*M

compartment*alpha_1*[C14140]
alpha_1 = 0.22
(C1) => (C2)

([C14141]) => ([C14141])
compartment*delta*C1

compartment*delta*[C14141]
delta = 0.05
(C1) => ()

([C14141]) => ()
compartment*beta*C1

compartment*beta*[C14141]
beta = 0.14
(A) => (T)

([C16522]) => ([treatment])
compartment*epsilon*A

compartment*epsilon*[C16522]
epsilon = 0.03
(T) => (A)

([treatment]) => ([C16522])
compartment*gamma_1*T

compartment*gamma_1*[treatment]
gamma_1 = 0.24
(T) => ()

([treatment]) => ()
compartment*gamma_2*T

compartment*gamma_2*[treatment]
gamma_2 = 0.293
() => (M)

() => ([C14140])
compartment*lambda/(1+rho*A)

compartment*lambda/(1+rho*[C16522])
rho = 1.0E-6; lambda = 3000000.0
(M) => ()

([C14140]) => ()
compartment*alpha_2*M

compartment*alpha_2*[C14140]
alpha_2 = 0.45
(C2) => (A)

([C14141]) => ([C16522])
compartment*delta*C2

compartment*delta*[C14141]
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).