Mathematical Analysis: Alcoholism and Its Relation to Health and Social Problems in Modern Society

This is a guest post by Patrick Bailey.

Man’s love affair with alcohol has existed ever since we first discovered the art of fermentation and distillation. In fact, the oldest fermented beverage can be traced back to 7,000 B.C. in China. Meanwhile, the practice of producing Sura, an Indian alcoholic drink made from rice, originated between 3,000 and 2,000 B.C.

Alcohol has always been associated with celebration and ceremonies. From ancient civilizations of the Sumerians, Babylonia, Greece, and Rome, you will find artifacts that proved their love affair with the spirits. There was even a point in history when alcohol was presumed to be a panacea, when in the 16th Century Britain recommended drinking for various illnesses. Alcoholism became prevalent by the 18th Century and the government moved to curtail distribution.

According to the study, 1 in 8 people in the US has a drinking problem. The survey studied 40,000 people in 2002 and 2003, and a decade earlier to get an extensive portrait of their behavioral patterns. Of the total, the instance of alcohol use disorder (AUD) occurred in almost half of them. During the second half of the study, the AUD increased by 12.7 percent. The number puts it at around 30 million people in the US who have a drinking problem.

The National Institute on Alcohol Abuse and Alcoholism shared the 2015 National Survey on Drug Use and Health, which found that more than 8 in 10 people who are 18 years and older consumed beer or liquor at some point in their lives, 7 in 10 drank the previous year, while more than 5 in 10 drank in the past month.

At the time of the study, 26.9 percent of the respondents said that they engaged in binge drinking in the previous month.

Binge Drinking Defined

The NIAAA says that a person is already binge drinking with 5 drinks for men and 4 drinks for women in a span of two hours. The blood alcohol concentration (BAC) level should be 0.08 g/dL.

The Substance Abuse and Mental Health Services Administration (SAMHSA) says that a person should be doing this at least once a month to be categorized as a binge drinker. A heavy alcohol user, meanwhile, would be binge drinking for five days or more in a month.

Low-risk drinking is defined as no more than 4 drinks for men in a day, and no more than 3 drinks in women in a day.

Prevalence of AUD in the United States

More than 15 million Americans 18 years old and older are suffering from alcohol use disorder, of which alcoholism is an integral part. Of that total, 9.8 million are males. However, only about 6.7 percent actually went to rehab to get treatment, which speaks volumes on how society generally views drinking.

Meanwhile, more than 600,000 Americans who are from 12 to 17 years old also have a drinking problem. Surprisingly, among the younger set, females outnumber the men or 325,000 against 298,000, respectively. The number of people in this set who are getting treatment is even less, with only a 5.2 percent rate.

The number of youth who are engaged in binge drinking is significant considering that when they start drinking before they are 15 years old they are twice as likely to develop alcohol dependence later in life.

In the United States, a little more than 88,000 Americans die from AUD-related causes. This makes alcohol use disorder the third leading cause of preventable diseases in the country.

According to the Centers for Disease Control and Prevention (CDC), alcohol-impaired driving claims an average of 29 lives a day. Meanwhile, the annual cost of these incidents is estimated to reach $44 billion.

The Economic Burden of Alcoholism

You may think that alcoholism is a personal thing. If a person is not hurting anybody else, then what he does with his life is nobody’s concern. However, mathematical analysis points to the contrary.

The CDC released a report which concluded that AUD is actually putting a huge burden on the country’s coffers. At the time of the study’s release in 2010, for instance, the amount lost to excessive drinking was estimated to hit $249 billion, or $2.05 for each bottle.

The economic burden was computed by accounting for lost productivity, health care expenses, motor vehicle crashes, and costs to criminal justice and law enforcement. Clearly, it’s not just a personal thing, considering that taxpayers’ money is involved.

Alcoholism: Mathematical Model

Mathematicians attempted to come up with mathematical models in order to establish behavioral patterns in the effort to find a viable and cost-efficient solution to the problem.

For instance, a Theoretical Analysis of Smoking and Alcoholism published in the Journal of Mathematical Modelling and Algorithms established a link between smoking cigarettes and binge drinking.

It found that smoking cigarettes will encourage one to drink. However, the reverse is not necessarily true. Therefore, in cases such as this, alcohol facilities work better when people are encouraged to quit their smoking habits first.

The study categorized society into several subsets:

  • Those who never touched cigarettes and a drink
  • Those who drink but never smoke
  • Those who smoke but never drink
  • Those who drink and smoke
  • Those who are addicted to cigarettes but not alcohol-dependent
  • Those who are alcohol-dependent but not addicted to cigarettes

As you can see, there are many gradients to the problem. But the mathematical model proves that getting a person to quit one first is the more feasible strategy.

Professors Hai-Feng Huo and Ying-Ping Liu of the Department of Applied Mathematics, in the Lanzhou University of Technology, pointed out that several mathematical models have been created on alcohol abuse and its link to societal problems and health issues.

Among these are:

  1. Drinking as an Epidemica— A Simple Mathematical Model with Recovery and Relapse (2007) by F. Sanchez, XH Wang, C. Chavez-Castillo, et al.
  2. Campus Drinking: An Epidemiological Model (2008) by JL Manthey, AY Aidoo, and KY Ward
  3. Modeling Alcoholism as a Contagious Disease: How ‘Infected’ Drinking Buddies Spread Problem Drinking (2007)
  4. Global Stability For A Binge Drinking Model With Two-Stages (2012) by HF Huo and NN Song
  5. Analysis of a Drinking Epidemic Model (2015) by S. Sharma and GP Samanta

The research by Sharma and Samanta is important because it attempted to answer the reasons for relapse and also introduce a treatment program based on the mathematical conclusions.

The relapse rate of alcohol is much higher compared to drugs (around 40 – 60 percent). Based on studies, 9 in 10 people with alcohol addiction tend to fall off the wagon within four years after completing rehab treatment.

However, alcohol facilities don’t really look at relapse as a negative thing. In fact, they consider it as part of the recovery process. Through the relapse, the person and the facility will develop insights into what they need to do to prevent a similar thing from happening again. Studying the conditions that contributed to the relapse will provide them with an understanding of the unique requirements of the patient concerned.

Alcohol abuse disorder should not be taken lightly. If you suspect that your loved one is dealing with alcoholism, seek help immediately.

Patrick Bailey is a professional writer mainly in the fields of mental health, addiction, and living in recovery. He attempts to stay on top of the latest news in the addiction and the mental health world and enjoy writing about these topics to break the stigma associated with them.

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4 thoughts on “Mathematical Analysis: Alcoholism and Its Relation to Health and Social Problems in Modern Society

  1. Navjeevan Rehabilitation center Patiala is home for people who wish to change their lives. Our therapeutic treatments are best suited to treat drug addicts and alcoholics. Allow us to be your ‘guiding light’ and find a way out of substance addiction.
    We have successfully tailored many alternatives to help people who have fallen prey in the world of drugs. Our services are organized to treat the mind as well as the body. We give behavioral counseling to our patients, understand their inner turmoil and help them overcome their fear of being carried away by drugs.


  2. What I think is that in majority of cases a person who drinks any amount of alcohol every day, is an alcoholic. But it is easy to check out. Just look at the skin condition, voice, manners, ageing. These are material indicators, the obvious ones. If these indicators are fine and the alcohol consumption doesn’t show on your face – etc, then go ahead, drink 🙂 But the thing is that it usually shows, and we just deny it.


  3. Good guest post, Edmark, and very informative. I was quite surprised that “low-risk drinking is defined as no more than 4 drinks for men in a day, and no more than 3 drinks in women in a day.” To me, 4 drinks in a day would be high risk, especially if one did it every day, but what do I know. Thanks for this …

    Liked by 1 person

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