The Perth Group
The HIV-AIDS debate

 Home

 What the Perth Group has argued

 Papadopulos redox theory of cellular function papers

 Papers and letters published in scientific journals

 Monograph on mother-to-child transmission

 Papers published in Continuum magazine

 Papers published in the popular press

 Papers/letters rejected by the scientific press

 Presentations

 Interviews

 Selected email correspondence

 TEMP

 Oxidation, Montagnier and the Perth Group

 Montagnier Nobel Prize 2008

 The Parenzee Case

 The House of Numbers

 Latest files

 Others

 Africa/South Africa

 Questions and answers

 Response to the NIH "Evidence" that HIV causes AIDS

 Translations of the Perth Group papers

 BMJ Online Debate

 Links

 Contacts

 About the Perth Group

 Perth Group at Virusmyth

 The Perth Group on YouTube

                                         

Calculation of the probability of HIV transmission between sexual partners

 

Also see:  http://bmj.com/cgi/content/full/324/7344/1034#resp3   This is a letter published in the BMJ arguing there is no proof of heterosexual transmission either in the West or in Africa.

 

Livio Mina.  Mathematician and Statistician, Department of Medical Physics, Royal Perth Hospital, Perth, Western Australia

 

Suppose that for each contact episode there is a constant probability, p of being infected which is independent of any previous contact history.

 

The number of contacts needed to first contract the disease follows the geometric distribution with probability function

 

                                    P(n) = p (1-p)n-1

 

where P(n) is the probability of first contracting the disease at the nth contact.

 

If we are interested in knowing the probability of having caught the disease after a given number of contacts (say n) we must sum all the probabilities of first catching the disease at the first, second, third, etc. contact up to n.  This is somewhat tedious, and for this question we can turn instead to the Binomial distribution which gives us the distribution of the number of times we would catch the disease (at least notionally) in n contact episodes.

 

The probability function here is

 

                                    P(x) =  n!/[x!(n-x)!]  px (1-p)n-x

 

where P(x) is the probability of being infected x times (sic) in n contacts.

 

The idea of multiple infection may not make a great deal of sense biologically but we can legitimately ask what is the probability that there be no infection at all ( ie. x = 0 ) after n contacts.  From the formula we see that this will be (1-p)n so that the probability of contracting the disease (regardless of the notion of multiple infections) is 1 -  (1-p)n.

 

This formula can be put into an EXCEL file (download here) in which these parameters can be varied to make the calculations.