What Can We Learn From A Crude Model Of Sexually Transmitted Diseases?

One of many STDs

It’s Statistical Modeling Day, so let’s look at one dealing with sexually transmitted diseases. Why this subject? Well, according to New York’s CBS 2, “Study Shows Soaring STD Rates In Many Areas Of New York City: 181 Zip Codes Analyzed And Surge In HIV/AIDS Is Alarming In Some Areas.”

The report said the Department of Health and Mental Hygiene canvassed the city’s neighborhoods for the “concurrence in rates of HIV/AIDS, chlamydia, gonorrhea, syphilis and hepatitis B, as well as two non-sexually-transmitted diseases — hepatitis C and tuberculosis.” TB is transmitted many ways, but “Hep C”, as it is affectionately known, passes all too often through drug use. However, there are too many transmission paths for these diseases for us to consider simply, so we’ll concentrate on STDs.

This are important, too, for as the report indicated:

The study said 33 percent of all the ZIP codes in New York City were in the top quintile citywide for multiple sexually-transmitted diseases during a survey taken in 2010. Among the most severe examples is ZIP code 10474 in Hunts Point, the Bronx, where rates of hepatitis C, chlamydia, gonorrhea and HIV/AIDS all ranked in the top 20 percent of all New York City ZIP codes.

Faring even worse was ZIP code 10457, in the Tremont section of the Bronx, which ranked in the top quintile for all seven diseases surveyed. Forty-three percent of residents in the neighborhood live below the federal poverty line, the report said.

Here’s our model. Suppose capital and lower-case letters represent the two sexes; it doesn’t matter which is which. Suppose A mates with a, B with b, and so forth, with the latter letters not mating with anybody (X,x,Y, and so on become priests, nuns, or New York Times subscribers). Also, an AA (so that we have more than 26 pairs of individuals) might even mate with another AA, etc. Let’s be clear: A does not mate with b, nor c with E. That is, once a letter matches its mate, it sticks to it and never switches.

We have the sexual mating piece, and now need the diseases. Sprinkle them liberally among our “people”, with fractions of HIV/AIDS, chlamydia, gonorrhea, syphilis and hepatitis B equaling that of reality. Maybe, say, 25% of our population have these diseases, let us suppose in equal amounts, and randomly.

This is a model, and therefore like all models only tenuously connected with reality; nevertheless if cautiously approached it can give us hints about reality—as long as we don’t take it too seriously.

Now if A has (say) gonorrhea, then a is likely to get it, too. But A (and a) can trundle off to the doctor and cure it. They might not, and so there is a chance that their offspring catch this disease through pregnancy. However, it’s not a sure thing; and then the offspring will probably seek out treatment (STDs are routinely screened for at pregnancy). HIV is different: it is not curable and can be passed to offspring (but only when capital and lower-case letters mate; if equally cased letters mate there are no offspring, of course).

B and b and C and c and even EE and EE etc. (suppose) have nothing. Since they have matched their letters, it is impossible they should catch anything—unless by the rare chance via drug use or contact with specimens. If, on these unlikely occasions one or both of the pair do contract a disease, they move to the category of A and a above.

Well, that’s it, really; that’s our entire model. You can see how far from reality it is, because if people stuck to the model, then STDs would rapidly die out or become as rare as cases of scurvy. A benefit not to be overlooked is the enormous cost savings of a program (even, yes, a government program, but better originating in the family) which encourages people to emulate the model.

But since I am a realist, and as I have already warned, there is no chance this model will ever hold for the entire population. Notice, though, that it can hold for subgroups of the population, even subgroups as small as “A and a.”

See? Something can be learned from this model after all.

Comments

What Can We Learn From A Crude Model Of Sexually Transmitted Diseases? — 11 Comments

  1. It would be an extremely rare event for there to be enough flu shots so that everyone could get one.

  2. >>This is a model, and therefore like all models only tenuously connected with reality; nevertheless if cautiously approached it can give us hints about reality—as long as we don’t take it too seriously.

    IOW, don’t hire you as no one should you seriously. What does a statistician do?

  3. MattS wrote, “It would be an extremely rare event for there to be enough flu shots so that everyone could get one.”

    But the number of doses produced has generally exceeded demand. So far this year 125.3 million doses have been distributed and in past years the totals have generally been greater than demand — 132.2 million doses in the 2011-2012 season and 163 million doses in the 2012-2011 season.
    http://www.cdc.gov/flu/professionals/vaccination/vaccinesupply.htm

    Although many adults (45.5%) and children (49.4%) were vaccinated during the 2011-12 influenza season, more than half of the United States population ≥ 6 months was not vaccinated against influenza. Continued efforts are needed to increase vaccination coverage, including:

    •Decrease racial and ethnic disparities: Racial and ethnic disparities remain among adults when compared with non-Hispanic whites. Continued efforts to increase vaccination coverage among adults in other racial and ethnic groups are necessary to decrease these disparities.

    •Implement proven strategies to increase vaccination coverage: Increased effort is needed to implement strategies necessary to increase influenza vaccination coverage during upcoming influenza seasons.
    http://www.cdc.gov/flu/professionals/vaccination/nfs-survey-march2012.htm

    End of Public Service Announcement.

  4. @Speed,

    US population is around 314,907,000.

    From your link.

    “•Currently, manufacturers project 135 million doses of flu vaccine to be produced this season.”

    135 million doses is not enough to vaccinate even half the population of the US.

  5. There for second I thought “The study said 33 percent of all the ZIP codes in New York City were in the top quintile citywide…” was an “all the children are above average” statement. Then I reread it and noticed the “… for multiple sexually-transmitted diseases during a survey taken in 2010.” Must have been one heck of a survey if all those people got multiple STDs from it.

  6. @Speed,

    Your original post says: “Has everyone had this year’s flu shot?”

    Limiting it to the US everyone would be 314 million people.

    You link from your first reply to me says that the expected total supply of flu vaccine for this year is 135 million doses.

    I think that there is a bit of a gap there.

  7. MattS wrote, “You link from your first reply to me says that the expected total supply of flu vaccine for this year is 135 million doses.

    I think that there is a bit of a gap there.”

    The objective is for availability to equal or slightly exceed demand — which it has. Difficult with long lead times.

    From the CDC: Influenza vaccine pre-booking typically occurs between January and March …
    http://www.cdc.gov/flu/about/qa/vaxsupply.htm

    More information on availability and distribution here:
    http://www.preventinfluenza.org/ivats/

    And before anyone asks, the cost per dose of adult flu vaccine is around a buck — a little less. Installation is extra. Quite a bit extra.
    I would like to believe this is wrong but I don’t think it is …
    Vaccine cost includes $0.75 per dose Federal Excise Tax

    http://www.cdc.gov/vaccines/programs/vfc/awardees/vaccine-management/price-list/index.html

    The Vaccine Injury Compensation Trust Fund provides funding for the National Vaccine Injury Compensation Program to compensate vaccine-related injury or death claims for covered vaccines administered on or after October 1, 1988.

    Funded by a $0.75 excise tax on vaccines recommended by the Centers for Disease Control and Prevention for routine administration to children. The excise tax is imposed on each dose (disease that is prevented) of a vaccine.
    http://www.hrsa.gov/vaccinecompensation/index.html

  8. @speed,

    It meets demand for now, largely because the government used to discourage people who were not at risk for dying from seasonal flu from getting vaccinated.

    There was story earlier this year about a company firing 150 employees for not getting flu shots. Granted this was a hospital operator in this case but that may change in the future.

    I work for an electric utility and my employer has been pushing all it’s employees to get vaccinated the last couple of years. There are no consequences for opting out for now, but that may change.

  9. IOW, don’t hire you as no one should you seriously. What does a statistician do?

    That’s just rude; and unless I’m missing a very poor joke, you missed the point of the quotation you used: “can give us hints about reality.”