Modeling the Effectiveness of Isolation Strategies in Preventing STD Epidemics

We formulate and analyze a two-group, selective-mixing, susceptible-infective-susceptible (SIS), sexually transmitted disease (STD) model where the infection-dependent desirability and acceptability in partnership formations are zero at high infection levels. We analyze two strategies to limit the spread of the epidemic by avoiding forming partnerships with people in a highly infected group. In one approach, the people in the highly infected group protect themselves by forming partnerships with only people outside their own group. We show that the transmission dynamics for this approach are similar to the situation where people continue to have both intragroup and intergroup partnerships. In the second approach, when one group becomes highly infected, the people in the other group adopt an isolation strategy and stop forming any partnerships with people in this highly infected group. We show that the second approach can limit the epidemic to the highly infected group. The other group will be infection-free, but as long as the epidemic in the total population exceeds the epidemic threshold, the epidemic will continue to persist. If the group reproductive number of the infection-free group is greater than one, and the infection should ever invade the infection-free group, then it will lead to an epidemic similar to the one that would have occurred if they had not isolated themselves from the other group. In this simple two-group model, although these isolation strategies may reduce the extent of an STD epidemic, they are ineffective in preventing an epidemic.