Increasing the infection risk early in an epidemic is individually and socially optimal under some parameter values. The reason is that the early patients recover or die before the peak of the epidemic, which flattens the peak. This improves welfare if the peak exceeds the capacity of the healthcare system and the social loss rises rapidly enough in the number infected. The individual incentive to get infected early comes from the greater likelihood of receiving treatment than at the peak when the disease has overwhelmed healthcare capacity. Calibration to the Covid-19 pandemic data suggests that catching the infection at the start was individually optimal and for some loss functions would have reduced the aggregate loss.
Infection arbitrage