Gambling Addiction Model

PS→S→I→S/D

Introduction

• Recent media coverage of gambling has recently increased its popularity by astounding numbers.– Ex. Poker has become one of the most popular forms

of gambling• Prize money for one tournament jumped from 5 million to 7.5

million in the past year because of its increase in participation

• To predict the change in gambling addiction in the United States, a modified version of the SIR model is used to model gambling addiction and predict the rate at which the pre-susceptible, susceptible, infected, and death populations of our model change over time.

Reasoning• A simple SIR model would not correctly illustrate

gambling addiction because many people commit suicide or experience a relapse in their recovery.

• Therefore, a P-S-S-I-S/D model is used– 4 group populations

• Pre-susceptible (PS): people who claim to have not gambled• Susceptible (S): people who have tried gambling but do not

have a problem• Infected (I): pathological and problem gamblers• Death (D): people who commit suicide due to large debts

from gambling

Statistics (U.S. Population)

• Pre-susceptible: 27% (approx. 80,668,100 people)

• Susceptible: 70% (approx. 208,367,792 people)

• Infected: 2.9% (approx.8,632,379 people)

• Death: 75,000 people (estimation)

Symptoms of an Addiction

• preoccupied with gambling (e.g. reliving past gambling experiences, planning the next venture, or thinking of ways to get money for gambling) 

• Need for increasing amounts of money for each bet to achieve the desired excitement

• repeated unsuccessful efforts to control, cut back, or stop gambling • restless or irritable when attempting to cut down or stop gambling • gambles to escape from problems or relieve a dysphoric mood (e.g., feelings of

helplessness, guilt, anxiety, depression) • Upon loss of money, gambler often returns another day to break even ("chasing"

one's losses)• deceives family members or others to conceal the extent of involvement with

gambling • illegal acts such as forgery, fraud, theft, or embezzlement to finance gambling • jeopardy or loss of a significant relationship, job, or educational or career opportunity

because of gambling • dependent on outside sources of finance relieve a desperate financial situation

caused by gambling.

Assumptions• The model encompasses all types of gambling• Treatment programs are short term (30-60

days) inpatient for gambling addiction recovery• 3000 people a year will commit suicide due to

gambling addiction• Data from individual states are a

representative samples of the U.S. population• Since there is no exact number of the number

of suicides due to gambling, assume the initial death population to be about 75,000, which is an estimate from collected data

• The current U.S. population is 297, 668 275.

Coefficients• a (transmission

coefficient)=.0000000001(estimated from 2.9%*about .0000003448% chance of becoming addicted if you come in contact with a problem gambler)

• b (recovery coefficient)=1/60 (average amount of days it takes to recover from gambling addiction)

• c (death coefficient)=3000/8632379/365 (amount of people who commit suicide from gambling per year/number of infected people/number of days in a year) = .00000095

• d (start gambling coefficient) = .00002

IVP’s• Initial Conditions

– PS(0)=80,668,100 – S(0)=208,367,792 – I(0)= 8,632,379 – D(0)=75,000

• Rate EquationsRate Equations– PS’ PS’ = -dPS(t) = -dPS(t) – S’S’=-aS(t)I(t)+bI(t)+dPS(t) =-aS(t)I(t)+bI(t)+dPS(t) – I’I’= aS(t)I(t)-(bI(t)+cI(t)) = aS(t)I(t)-(bI(t)+cI(t)) – D’D’=cI(t) =cI(t)

Graph of Gambling AddictionGambling Addiction Model

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Results• As time increases, the populations of each

group level out to a point where about 56 million people are addicted to gambling

• 170 million people have gambled but are not problem gamblers

• 75 million people never gamble

• 266 thousand people have committed suicide.

Analysis• With gambling gaining rapid popularity and becoming

a dominant force displayed in the media, it is possible that this degree of gambling problems does arise.

• It is speculation at this point because it is unclear whether it would ever level out and at what amount of people

• There are so many other factors involved in why people gamble and how gambling addiction begins, that the modified SIR model cannot even begin to explain how the problem will continue over the next decade.

• It would require a far more complex model to correctly display the behavior of the gambling population as time goes on

Conclusion