Before revision:  We compare different strategies: do-nothing , social distancing , reduction of social mixingand lockdown, assuming that there is no vaccine and no efficient medicine .
After revision:  We compare different strategies: do-nothing ' strategy with mitigation strategies based on social distancing and reducing social mixing. We study epidemics in the pre-vaccine era, where immunity is obtained only by infection. The model applies only to epidemics for which reinfections are rare and can be neglected .