We introduce two types of agent heterogeneity in a calibrated epidemiological search model. First, some agents cannot afford staying home to minimize their virus exposure, while others can. Our results show that these poor agents bear most of the epidemic’s health costs. Moreover, we show that having more agents who do not change their behavior during the pandemic could lead to a deeper recession. Second, agents are heterogeneous in developing symptoms. We show that diseases with higher share of asymptomatic cases, even if less lethal, lead to worse health and economic outcomes. Public policies such as testing, quarantining, and lockdowns are particularly beneficial in economies with a larger share of poor agents. However, lockdowns lose effectiveness when part of the agents take precautions to minimize virus exposure independent of government actions.