There is a small gap in between my apartment's front door and the door frame. I was told by an exterminator that small roaches may be able to fit through the gap to get inside, and it seems that may be the case given the fact that I sometimes find roaches close to the door. Part of what may be causing the gap is that the metal door isn't fully touching the door frame when it is closed. The advanced age of the door may be a contributing factor.
With respect to possible solutions, I was considering placing an adhesive rubber door gap filler strip around the edges of the door (inside the apartment), but it seemed that that might be unsightly and may not actually prevent roaches from coming through. I was also, thinking about putting some kind of substance (like silicone) in the gap on the outside of the apartment, but was thinking that adding something like that may be a little messy and might not hold up with the constant opening and closing of the door.
What would be the best way to fill the gap? Note: The door frame is metal and the surrounding wall is concrete.
Outside of the door:
Inside of the door: