The cumulative effect of risk compensation on infection preventive measures

We study several epidemic models (with and without gender structure) that incorporate risk compensation behavior in response to a lower chance of acquiring the infection as a result of preventive measures that are only partially effective. We show that the cumulative risk compensation that occurs between a high risk susceptible and infectious individual may play an important role in whether the implementation of these measures is successful in lowering the epidemic reproductive number. In addition, we show that certain levels of risk compensation may cancel the benefit of the low infection risk practiced by diagnosed infectious individuals when the goal is a reduction of the epidemic reproductive number.