> We develop a multi-risk SIR model (MR-SIR) where infection, hospitalization and fatality rates vary between groups—in particular between the “young”, “the middle- aged” and the “old”. Our MR-SIR model enables a tractable quantitative analysis of optimal policy similar to those already developed in the context of the homogeneous- agent SIR models. For baseline parameter values for the COVID-19 pandemic applied to the US, we find that optimal policies differentially targeting risk/age groups sig- nificantly outperform optimal uniform policies and most of the gains can be realized by having stricter lockdown policies on the oldest group. For example, for the same economic cost (24.3% decline in GDP), optimal semi–targeted or fully-targeted poli- cies reduce mortality from 1.83% to 0.71% (thus, saving 2.7 million lives) relative to optimal uniform policies. Intuitively, a strict and long lockdown for the most vulnera- ble group both reduces infections and enables less strict lockdowns for the lower-risk groups. We also study the impacts of social distancing, the matching technology, the expected arrival time of a vaccine, and testing with or without tracing on optimal policies. Overall, targeted policies that are combined with measures that reduce inter- actions between groups and increase testing and isolation of the infected can minimize both economic losses and deaths in our model.
