Policy During an Epidemic With Super-Spreaders

I study mitigation policies during an epidemic when individuals vary in their degree of interaction with others. Individuals with a high degree are more likely to contract the disease and, once infected, they transmit the disease to more individuals in expectation. Thus, the presence of high degree individuals fuels the epidemic initially. However, this also means that the high degree individuals are more likely to become immune, and this lowers the reproduction number relatively quickly. That the buildup of immunity is correlated with social interactions has implications for policy. In an SIR model I compare a lockdown in which all individuals are forced to have the same degree with a more liberal policy in which the degree is lowered proportional to the original degree. The lockdown has to be in place longer than the liberal policy to limit the number of deaths to the same extent. The reason is that under the lockdown the high degree agents do not build up immunity faster than the low degree agents. When the policy is lifted, these high degree agents will fuel a second wave of infections. Under the liberal policy, average immunity is the same as under the lockdown, but degree-weighted immunity is larger, leading to a less severe second wave once policy is lifted. I show that the same implications for policy hold in a model with economic behavior