• Circumcision;
  • Coinfection;
  • Condom usage;
  • Female-to-male transmission probabilities;
  • Herpes simplex virus type 2;
  • Human immunodeficiency virus;
  • Infection;
  • Markovian models;
  • Maximum likelihood estimation;
  • Relative risk;
  • Sexually transmitted agent

Summary.  To study the interactions between two sexually transmitted diseases without remission of the infections, we propose to use Markovian models. One model allows the estimation of the per-partnership female-to-male transmission probabilities for each infection, and the other the per-sex-act transmission probabilities. These models take into account the essential factors for the propagation of both infections, including the variability according to age of the rates of prevalence in the population of female partners for the male individuals constituting our sample. We estimate transmission probabilities and relative risks (for circumcision, usage of condoms and the effect of one infection on the infectivity of the other) by using the maximum likelihood method. Bootstrap procedures are used to provide confidence intervals for the parameters. We illustrate the new procedures with the study of the interactions between herpes simplex virus type 2 and human immunodeficiency virus by using data from the male circumcision trial that was conducted in Orange Farm (South Africa). The study shows that the probability that a susceptible male individual acquires one of the viruses is significantly higher when he is already infected with the other. Using the Akaike information criterion, we show that the per-partnership model fits the data better than the per-sex-act model.