We have heard from a biostatistician, an epidemiologist, and a mathematical modeller. This is the combination that is necessary to advance our enterprise of analyzing the reality that transmits infections through populations. It was great to have them on the same podium. It is great to have them meeting in discussions over tea. It would be even greater to have them working together on joint projects.

Julian Peto has presented us with an example of a chronic infectious disease where the need to combine the principles of infectious and chronic disease analysis is clear. HPV is a chronic infection where the course and outcome of the infection are dependent upon numerous host and agent specific factors. Even before the agent of cervical cancer was determined, the sexual mode of transmission was made clear as the number of partners of the victim and of the victim's spouse were both related to the risk of disease. Now that the agent has been determined, we can proceed to work out the determinants of transmission of that agent in ways that should help better to orient prevention programmes. We can begin to assess what aspects of sexual contact patterns and of host immune responses affect the level of disease in a population. We can then begin to plan both behavioural and biological interventions to prevent disease.

To work out transmission dynamics, we also need to understand the natural history of infection and how infection gets translated into disease and into contagiousness. As Julian Peto suggests, the natural history of HPV is complex and heterogenous.

The long incubation period of AIDS, with variation in infectiousness over its course, has emphasized the need to model progression of the disease process. The models used for progression of HIV infection to AIDS have generally been staged Markov models that imply a one-way progression from infection to AIDS to death and so do not allow for temporary remissions in the progression of the disease. Such models have negative exponential distributions for the transit times in a stage and independence of transit times in successive stages (Longini et al. 1992, Longini et al. 1991). In our studies to estimate transmission probabilities from data on the Chicago MACS cohort, by stage of infection, we found it necessary to examine progression in the cohort.

The Multicenter AIDS Cohort Study (MACS) involves 4 cohorts of male homosexuals recruited in 1984 in 4 cities: Baltimore, Chicago, Los Angeles and Pittsburgh (Kaslow et al. 1987). Approximately every 6 months, the participants had physical examinations, had blood drawn and filled out a questionnaire on sexual practices. We examine progression in the Chicago MACS cohort which consisted of 1020 individuals at the start of the study. We present data on the first to twelfth waves of examinations, covering the period 1984–90.

Cumulative plots of seropositivity for HIV-1 show that approximately 40% of the Chicago cohort was HIV(+) by the first wave and that about 70 more seroconversions occurred from wave 1 to wave 12. The experience of the other cohorts was similar. Thus roughly 85% of the infections occurred before the first wave of examinations.