In the previous session, we described the effects of host age on transmission of respiratory and other directly transmitted infections, such as influenza and pneumococcal disease. In this one, we’ll consider a different form of host heterogeneity: for sexually transmitted diseases, we focus on heterogeneity between people in their sexual risk behavior. Empirical studies have shown that while some people have many sexual partners each month or even week, others have many fewer sexual partners. For a sexually transmitted infection, those who have many sexual partners are both more likely to become infected, because they have more chances of being exposed to an infectious partner, and more likely to infect others once they are infected, because they have more opportunities to transmit to susceptible partners. This form of heterogeneity is particularly important in maintaining the transmission of an infection in a population. We discussed the idea of a core group for infection in the last session but the idea of a core group actually arose in the context of sexually transmitted infections. In a population where most people are monogamous or have a small number of sexual partners, it is hard to understand how infections transmitted by sexual intercourse can be maintained, because as we learned earlier, an infection can only be maintained if the average infectious person has more than one infectious contact that can transmit infection to another person. Epidemiologists studying gonorrhea in the 1970’s were puzzled because the numbers didn’t seem to add up given the number of partners people reported on average, the duration of infectiousness with gonorrhea, and the risk of transmission per partnership. They didn’t understand how the average case could infect more than one other case. The solution, they realized, was that the average didn’t tell the whole story. Some people, the rare individuals who had many partners, were especially likely to get infected with gonorrhea, and also especially likely to have many contacts to pass it on to. In mathematical terms, epidemiologists later figured out an elegant way to express this effect. If everyone had the same rate of acquiring partners, c new partners per year, and if they remained infectious for a time D, and had a probability beta of passing on infection during the course of a partnership, then on average they would infect c times beta times D new partners, if they became infected. The basic reproductive number R0 would be c times beta times D, and the disease could spread if R0 was greater than one. But if there were some high-risk people and other low-risk people, with different rates of partner acquisition that averaged out to c, then the basic reproductive number would be beta times D times c-hat, where c-hat was the so called “effective average” rate of partner acquisition. c-hat is not just the mean, or a regular average, but is the mean value of c plus the variance of c divided by the mean of c. This effective average is always bigger than the mean. To recap, when there is a form of host heterogeneity that affects both the rate of becoming infected and the rate of transmitting if infected, then the high-risk group becomes disproportionately important and the total transmission is more than one would expect from the average. Another factor that can further boost the ability of an infection to persist in a population is assortative mixing, that is, when high-risk people tend to partner with other high-risk people. Together, heterogeneity and assortativeness help to constitute core groups in sexually transmitted infections - those groups that have more sexual partners than average and pick those sexual partners from within the group. In this way, the theory of heterogeneity in respiratory infections and in sexually transmitted infections is similar; although respiratory infections are transmitted mainly by children and sexually transmitted infections mainly by adults, heterogeneity and assortativeness in contacts help to maintain transmission within the population. The implications for control are similar too. With either type of infection, interventions that slow transmission within the core group can be especially effective in many circumstances, with benefits that extend to the whole population.