The Odd Epidemiology of AIDS

Thomas Keske TKeske at
Mon Mar 27 18:59:01 EST 2000


Recently, I have been trying to collect data and write software for
the purpose of modeling the AIDS epidemic.

It quickly becomes apparent that AIDS is a very strange epidemic,
and a difficult one to model.  Necessary data such as infectivity
rates or average numbers of partners can be inconsistent and
varying widely.

There is at least one clear message, however, that is relevant to
the health of the gay community.  If you have sex with a person who
is HIV+, your chances of becoming infected might be very widely
variable.   When you hear a flat-rate figure quoted, such as
on the risks of oral sex, it is an average that might be

This point, while it has been made before, has probably not been
emphasized enough.

There is also another likely implication. If the most recently
published figures for infectivity rates are accurate, then the
"Patient Zero" scenario is quite unlikely.  I.e., the AIDS
epidemic in gay men did not likely begin with a single, infected
person.  More likely, it would have began with a simultaneous,
mass-infection of a larger group of men.

Below are estimates for the probability of infection,
per contact [1]:

      anal receptive:  0.0082 (known HIV+ partner)
      anal active:     0.0006 (HIV+ or unknown partner)
      oral receptive:  0.0004 (HIV+ or unknown partner)

The above figures are based on a study of 2,189 high-risk men,
tracked over 2,633 person-years.

Oral "active" role (being fellated) is not mentioned, but is
presumably near zero,  because the real risk is associated with
exposure to semen ("receptive" role).

Some news articles have confused probabilities expressed as
percentages and as decimal fractions.  Typically, probabilities are
expressed as a value between 0 and 1.  E.g. probability = .5 would
be 50%, or probability = .0082 would be .82%.

A number of studies mention high rates of variability in
infectivity.  Another 1989 study from Harvard School of Public
Health [2] listed the risk of receptive anal sex in the range
of .005 to .03.   This was a smaller scale study of
155 partnerships.

Another 1994 study by University of Michigan [3] purported to show
time-varying rates of infectiousness, depending on the stage
of infection of the HIV+ partner.  The first few weeks of infection,
after initial HIV exposure, were claimed to be up to 1000-3000 times
more infectious than the long, asymptomatic period (lasting on the
order of a decade).   Probabilities of infection were claimed to be
up to 0.3 per anal contact during the "primary infection" stage,
then dropping as low as 0.0001 during the asymptomatic period.

The authors make the following statements as to why they
postulate such extremely high infectivity during the first
few weeks of infection:

   "Thousandfold differences in transmission probabilities
    by stage of infection are needed to fit the epidemic curves"

   "The pattern of high contagiousness during the primary
    infection followed by a large drop in infectiousness may
    explain the the pattern of epidemic spread in the early
    years of the epidemic."

   "Such a role for early infection is necessary
    to explain the fall off in the rapid rise of the epidemic."

In other words, they are trying to explain why such a large
explosion of gay men became HIV+ in the early 1980s, followed
by a sharp dropoff even in the "high-risk" subgroups who did
not practice "safe sex".

This points to a possible circularity in the modeling: the
probabilities of infection are calculated to fit the
observed shape of the curve.  You cannot then use the same
model to determine whether the curve "makes sense", or whether
there might be some other factor responsible for a mass "seeding"
of the epidemic.

To resolve this, more data is needed from subjects whose
HIV status and sexual activities can be closely tracked,
to verify if the infectivity is in fact as high as claimed.

It could also be studied to see if differences in viral load
are adequate to explain the thousandfold differences in

The authors explain that without their hypothesized differences
in infectiousness, the growth of the AIDS epidemic would have
been much slower than actually observed:

   "If the probability of transmission were constant for 10 years
    and the final endemic level reached 6%, it would take 1150
    years after the first infected arrived to reach 3% infected.

    Higher endemic levels are reached more quickly given constant
    transmission probabilities.  But even there, constant
    infectivity is unrealistic.  If the endemic level reached
    is 68%, it would take 76 years to reach 34%."

I have not been able to determine yet exactly how the authors
derived those figures.

However, I had been writing my own modeling program, and had
been independently reaching a similar conclusion: if you start
with a single infected person, it appears that the development
of the AIDS epidemic would have been a much longer, drawn-out
process than what we saw.   By the time that full-blown AIDS
cases were observed, you would not have had such a large percentage
of the community infected.

The program lets you define a population size, how many initially
infected, what types of sex they have, and how often.   It
randomly pairs partners, and keeps track whether each person
is currently infected.  If an uninfected man has contact
with an infected man, then the program infects him at random,
but strictly within the probability bounds of the stated
infection rates.

I projected for a gay male population roughly the size of San
Francisco, with similar sex patterns.

A study by Dr. George F. Lemp [4] estimated about 43000 - 69000
openly gay males in SF, settling on a middle figure of 56000.

Another study [5] states that gay males reporting to a San Francisco
VD clinic were averaging 67 partners per year.   Since these are
high-risk men, this figure should be adequate as an upper limit
to apply to the general population.  This study also reported that
nearly all men reported a mix of both anal and oral sex.

I tried testing a population of 56000 men, having an equal mix
of anal/oral sex, with 67 partners per year starting
with one person infected, and projecting forward for 20 years.

After 20 years, you get only about 1.2% of the population infected
(700+ of the 56000).

It took only few dozen cases of full-blown AIDS before we
knew that we had a problem. A fair number of men progress
to full-blown AIDS in 5 years or less.   Therefore, we should
have seen a much smaller percentage of the population infected,
by the time that we noticed the first AIDS cases.

A wildly varying infectivity rate might be one possible explanation
for the difference.  A mass "seeding" of the epidemic, causing
many men to become infected nearly simultaneously, would be
another possibility.

However, it seems clear that something is probably wrong
either with the flat infectivity rates, or with notion of
a single "Patient Zero".

Until that is resolved, the gay community would be well advised
not to trust entirely as to the meaning of the flat infectivity
rates.  These may necessarily be "wrong", so much as they
might be deceptive if interpreted too simplisticly

It would also be well-advised to be open-minded about the
possibility that this epidemic was mass seeded by some
means, such as by vaccines.

A sample of the modeling program output is appended below.

The modeling program can run on a PC with Microsoft Visual C++.
If anyone wants to run it, please let me know.  I am debugging
a more complicated version that handles time-varying infectivity
rates and arbitrary risk subgroups with different behaviors.

Tom Keske
Boston, Mass.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

[1] Am J Epidemiolo 1999 Aug 1;150(3):306-11
    Per-contact risk of human immunodeficiency virus transmission between
    male sexual partners.  Vittinghoff E, Douglas J, Judson F, McKirnan D,
    MacQueen K, Buchbinder SP.  Dept. of Epidemiology and Biostatistics,
    University of California

[2] J Clin Epidemiol 1989;442(9):849-56
    Infectiousness of HIV between homosexual partners.
    DeGruttola V, Seage GR 3d, Mayer KH, Horsburgh CR Jr
    Dept. of Biostatistics, Harvard School of Public Health

[3] J Acquir Immune Defic Syndr 1994 Nov;7(11):1169-84
    The role of primary infection in epidemics of HIV infection in
    gay cohorts.  Jacquez JA, Koopman JS, Simon CP, Logini IM Jr
    Dept of Physiology, University of Michigan

[4] Lemp GF, et al Projections of AIDS morbidity and mortality
    in San Francisco.  JAMA 1990 Mar 16;263(11):1497-501
    PMID:2407871; UI:90172481

[5] Godfried J.P. van Griensven, et al, "Epidemiology of
    Human Immunodeficiency Virus Type 1 Infection among
    Homosexual Men Participating in Hepatitis B Vaccine
    Trials in Amsterdam, New York City, and San Francisco,
    1978-1990.   American Journal of Epidemiology, Vol 137
    No. 8, 1993

** NOTE: for the program execution below, I'm using a more
         conservative estimate that BOTH men have higher-risk
         "receptive" anal/oral role in the same "contact".
         Thus, I use the higher "receptive" rate for both active
         and passive.

Enter Population Size ( <= 100000): 56000
Enter number initially infected: 1
Probability, infection per ACTIVE  contact, type #1: .0082
Probability, infection per PASSIVE contact, type #1: .0082
Probability, infection per ACTIVE  contact, type #2: .0006
Probability, infection per PASSIVE contact, type #2: .0006
Enter average number of contacts per year: 67
Enter number of years: 20
Enter random seed (any number between 1 and 4294967295): 1341234
New infections in year #1 = 0, GRAND TOTAL = 1
New infections in year #2 = 1, GRAND TOTAL = 2
New infections in year #3 = 1, GRAND TOTAL = 3
New infections in year #4 = 0, GRAND TOTAL = 3
New infections in year #5 = 3, GRAND TOTAL = 6
New infections in year #6 = 2, GRAND TOTAL = 8
New infections in year #7 = 6, GRAND TOTAL = 14
New infections in year #8 = 8, GRAND TOTAL = 22
New infections in year #9 = 7, GRAND TOTAL = 29
New infections in year #10 = 12, GRAND TOTAL = 41
New infections in year #11 = 8, GRAND TOTAL = 49
New infections in year #12 = 22, GRAND TOTAL = 71
New infections in year #13 = 17, GRAND TOTAL = 88
New infections in year #14 = 34, GRAND TOTAL = 122
New infections in year #15 = 27, GRAND TOTAL = 149
New infections in year #16 = 63, GRAND TOTAL = 212
New infections in year #17 = 82, GRAND TOTAL = 294
New infections in year #18 = 108, GRAND TOTAL = 402
New infections in year #19 = 138, GRAND TOTAL = 540
New infections in year #20 = 165, GRAND TOTAL = 705


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