Can't you just send out test kits to 10000 random Italians and then use that to calculate the number of infected people? If its really common then you'd find 100-1000 infected people and then you can calculate the real mortality rate simply by monitoring them and recording how many of them have died. Of course it is possible that proper medical care results in a much lower than usual mortality rate compared to untreated people but that sounds more like good news than bad news.