On the importance of risky behavior in the transmission of sexually transmitted diseases

We consider a population with two types of individuals: those who engage in risky sexual behavior (the core) and those who do not (the majority). We are interested in the situation where the majority would not be able to sustain an epidemic without the presence of a core. We show that even if the core is randomly spread out in the general population and is very infectious there will be no epidemic if the proportion of individuals in the core is below a certain threshold (that depends on the infection rates). Risky behavior does put the whole population at risk but only if the behavior is widespread enough. This gives support to the idea of concentrating resources to fight sexually transmitted diseases on the core group in order to lower the proportion of individuals in the core. We show our results for two models: one with total mixing and the other with limited mixing.