Sunday, October 05, 2014

The Ebola Epidemiology They Won't Talk About

Remember the AIDS epidemic?  I mean back when AIDS was Big News in part because it was New and in part because it was actually rapidly spreading during the late 1980s.  Well there was this rumor going around the midwest that "the AIDS epidemic is over".  It was more than a rumor, though; It made it into newspapers -- in particular college newspapers where the rumor's optimism could potentially do the most damage by encouraging sexually active young adults to let down their guard so to speak.

Guess where that rumor started?

The world's most prestigious science magazine:  Nature.

Guess where that rumor ended?


No, really; I ended it.

I won't go through all the details of this bit of history here.  I will, however, focus on the correct arithmetic formulas describing the AIDS epidemic and then proceed to describe a way current "authorities" may be underestimating the dangers of the current, unprecedented, Ebola outbreak.

One of the errors the general public made in thinking about the AIDS epidemic was corrected by May RM, Anderson RM in Transmission dynamics of HIV infection*, Nature. 1987 Mar 12;326(6109):137–142.  That error is to over-simplify the transmission dynamics of the virus.  The oversimplification is to assume that the number of people an infected person will infect is proportional simply to the average number of sexual partnerships per person infected with HIV.  

The actual formula is:

R0 = βcD


R0 = Reproductive rate of the virus ( If > 1 we are in an epidemic.)
D = Duration of infectiousness
β = The odds of transmitting the virus per partnership

So far so good, right? I mean the longer you are infectious the more people you are likely to infect and the more likely you are to infect a given partner, the more people you are likely to infect.

But what about that 'c' up there? Well, here it is in all its complex glory:

c = m + σ²/m


c = The effective average number of partnerships per person over the distribution
m = The average number of partnerships per person over the distribution
σ = The standard deviation in the number of partnerships* per person over the distribution

The big enchilada of epidemiology is determining R0 for a given population. The big enchilada of public health is getting R0 as low as possible -- most urgently below 1 and most desirably 0. One of the things that can make people over-optimistic about R0 is thinking 'c' is 'm' when, in fact, 'c' is bigger than 'm'. Indeed, if σ is large, the smaller 'm' is the bigger 'c' hence R0 is.  

Oh, but its worse than that!  

Did you notice that 'σ' is squared: σ² (aka "variance" in the number of partnerships per person)

You know what that means?

It means "diversity is strength" squared. Strength of the epidemic squared that is!

It is known that during the AIDS epidemic there have been AIDS murders; someone with AIDS simply "loses it" and starts having sex -- deliberately unprotected sex -- with others to infect them. Indeed, AIDS neuropathy may contribute to such serial-killer-by-sex behavior in some cases.

There are people who harbor profound feelings of resentment if not outright hatred of US society. Do you think that number has decreased since 1987 when the above epidemic formulas were derived for AIDS? Has the "diversity" of US society decreased since 1987?

I'll put it this way:

If, on average, one of those serial-killer vectors has Ebola and is able to "scan" enough of the population (say, by boarding a subway and leaving a lot of bodily fluids around) to infect another of those vectors, civilization is in big trouble.

*That was the article that I, in turn, further corrected to end the rumors that "the AIDS epidemic was over".  My correction was merely to the definition of one of the variables -- a correction that was later published by Nature in a quasi-retraction -- that being "the probability of transmission of the HIV per partner contact" vs "the probability of transmission of the HIV per partnership".  A "partnership" is a sexual relationship regardless of the number of sexual acts within that relationship.  As Robert M. May told me in our conversation, the tendency to transmit was more dependent on the particular two people in a relationship than it was on the number of times they had sex.  I know -- its counter-intuitive but that's really what he said.  My suggested change to the formula was to keep "the probability of transmission per partner contact" as the definition of β but to exponentially approach 1 with the number of sex acts. He told me that's not an accurate model of the probability and although I don't understand why, I can accept that he did have the proper background to make that judgement. In any event, his is a better definition of a "hit and run" type of encounter between members of the public in anonymous urban settings, which is the primary problem in the Ebola epidemic.