# MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
10/2007

### The probability of HIV infection in a new host and its reduction with microbicides

Henry Tuckwell, Patrick Shipman and Alan Perelson

#### Abstract

Objective: To estimate for transfer of a given quantity of HIV virions, the probability of infection and the time window for post-exposure prophylaxis (PEP). For sexual intercourse, to estimate the percentage reduction in the probability of HIV infection when the number of virions transferred is reduced and hence determine the usefulness of microbicides of various efficacies.

Methods: We use a simple mathematical model to estimate the probability and its time dependence that one or more virions successfully infect target cells.

Results: For heterosexual transmission, a parameter γ is employed which is a measures the strength of the infection process. For the smaller value of γ the Pinfection is from 6 x10-5 to 0.93 or from 7.82 x 10-6 to 0.29 where the lower figures are for the transfer of 100 virions and the upper figures are for the transfer of 4.4 million virions. For microbicides we estimate that reductions in Pinfection with the stated efficacy may apply when the number of virions transferred is less than 105, but declines to zero for viral loads above that number. We also give estimates of Pinfection for needlestick transfer and the time window for PEP.

Conclusions: PEP should always be applied immediately after a needlestick incident. A microbicide may reduce Pinfection in a new host by its stated efficacy only when the number of virions transferred is less than about 105. Manafacturers of microbicides should be encouraged to report their effectiveness at various transferred viral burdens.

24.01.07
Published:
24.01.07
MSC Codes:
62P10
Keywords:
HIV, stochastic model, Prevention

### Related publications

inJournal
2008 Repository Open Access
Henry C. Tuckwell, Patrick Shipman and Alan Perelson

### The probability of HIV infection in a new host and its reduction with microbicides

In: Mathematical biosciences, 214 (2008) 1-2, pp. 81-86