Before revision:  We prove that the infected always want to make more contacts than the level at which it would be socially optimal, which reinforces the need to reduce contacts of the infected (e.g. quarantining, sick paid leave).
After revision:  We prove that the optimal decision of the infected is always to make more contacts than the level at which it would be socially optimal, which reinforces the need to reduce contacts of the infected (e.g. quarantining, sick paid leave).