Behavior Changes in SIS STD Models with Selective Mixing

We propose and analyze a heterogeneous, multigroup, susceptible-infective-susceptible (SIS) sexually transmitted disease (STD) model where the desirability and acceptability in partnership formations are functions of the infected individuals. We derive explicit formulas for the epidemic thresholds, prove the existence and uniqueness of the equilibrium states for the two-group model and provide a complete analysis of their local and global stability. We then investigate the effects of behavior changes on the transmission dynamics and analyze the sensitivity of the epidemic to the magnitude of the behavior changes. We verify that if people modify their behavior to reduce the probability of infection with individuals in highly infected groups, through either reduced contacts, reduced partner formations, or using safe sex, the infection level may be decreased. However, if people continue to have intragroup and intergroup partnerships, then changing the desirability and acceptability formation cannot eradicate the epidemic once it exceeds the epidemic threshold.