What illness does poor hygiene cause in modern cities?

Dental Decay. Poor dental hygiene relates to higher rates of cardiovascular desease and stroke. The simmering, low grade gum infection or gingivitis activates a body wide inflammatory reaction. The inflammatory cells and its immune chemicals will target tissue away from the teeth too. The small vessels of the heart and brain are affected long term causing heart disease and stroke.
Spread of infections. This is a very general question, but in general poor hygiene allows for the uncontrolled growth and in turn spread of bacteria and other infectious agents. These can be passed from person to person in any number of ways. Regular hand washing, care to open wounds and sores and good dental hygiene are great places to focus in order to minimize these issues.