title: Plausible and implausible parameters for mathematical modeling of nominal heterosexual HIV transmission.
abstract: OBJECTIVE
  Several mathematical models simulate a HIV/AIDS epidemic by using the assumption that heterosexual transmission is the major or sole transmission mode. The validity of these models has been unclear. To understand the validity of these models, empirical estimates for relevant model parameters are needed that can be compared with parameters used in mathematical models.
  
  
  METHODS
  A brief review of per-contact transmission probabilities based on HIV-discordant, monogamous couples is provided, and sources of bias in transmission efficiency estimates are discussed. Average number of partnerships and the distribution of partnerships are estimated for seven sub-Saharan African countries. Distribution parameters are fitted to the Poisson distribution, negative binomial distribution, and the discrete Pareto (Zipf) distribution, using the maximum likelihood method. The Pearson chi2 test statistic is used to measure goodness of fit, and the Akaike and Bayesian information criteria are also provided. To balance the reported number of partnerships, missing number of prostitutes is estimated. These empirical estimates for relevant model parameters are compared with parameters used in representative models of nominal heterosexual HIV transmission in Africa.
  
  
  RESULTS
  Reported transmission efficiencies (unadjusted for competing exposures that inflate estimates) per sexual episode range from 0.0003 to 0.0012. Average number of partnerships is less than 1.5 in all countries. The discrete Pareto distribution fits the data better than the Poisson or negative binominal distribution. In almost all countries, female reported number of partners follows a discrete Pareto distribution. To close the sex disparity gap in number of partnerships, between 0.13% and 0.69% of the female population would need to be classified as prostitutes. Comparing these estimates with the parameter values used in existing mathematical models shows that existing models use grossly inflated per contact transmission efficiencies or rely on implausible assumptions regarding contact frequency, which results in implausibly high per-partner transmission rates. Assumptions regarding average number of partners are too high, and the distribution of partnerships is not supported by available data. As a consequence, existing mathematical models overestimate nominally heterosexually transmitted HIV infection in sub-Saharan Africa.
  
  
  CONCLUSIONS
  Existing models of nominal heterosexual HIV transmission for sub-Saharan Africa rely on assumptions inconsistent with empirical evidence. Simulations have not accurately portrayed the epidemiological situation in sub-Saharan Africa, and conclusions drawn from these models should be interpreted with great caution. To realistically simulate HIV spread in sub-Saharan Africa's general population nominally due to heterosexual HIV transmission, parameter values should be based on the most accurate data.
authors.affiliation: Department of International Economic Policy, University of Freiburg, Germany.
authors.forename: Eva
authors.initials: E
authors.lastname: Deuchert
authors.forename: Stuart
authors.initials: S
authors.lastname: Brody
mesh_terms: D017954:Africa South of the Sahara / Q000453:epidemiology; D003198:Computer Simulation; D005260:Female; D015658:HIV Infections / Q000453:epidemiology* / Q000635:transmission*; D020010:Heterosexuality; D006801:Humans; D008297:Male; D015233:Models, Statistical; D011336:Probability; D015203:Reproducibility of Results; D011477:Sex Work / Q000706:statistics & numerical data; D012747:Sexual Partners