The only area where malaria is a concern is in the Darien, deep jungle area bordering Colombia. There hasn’t been a case of malaria in decades in the others areas but if you are planning to go to the Darien, you should definitely take with you anti-Malaria meds.
The last victim of yellow fever in the Canal Zone (which includes Panama City) died in 1906.
The only mosquito you need to be concerned about is the one that packs Dengue Fever. Unfortunately, there is no prophylactic med for Dengue. The best prevention is a repellent with at least 40% deet, and long sleeved shirts and long pants when hiking in the jungle.