popperik: You can get some info on that in one of the statistics views (the one with the pie chart). Basically the more they like your hospital, the more of them will come.
As for less patients, I never really wanted that. Either I had enough money so I could keep on building stuff for more patients, or I didn't have enough money and I wanted more patients to come :) You could always just send them to different hospitals though (or home).
but how is it possible to get barely any patients at the start of the game. my case was in the first 3 years i got just over 50 patients in total. i did not have bad rep since it is not even possible to have that bad rep at the start.