Playing this game is about solving the puzzle – so if you haven’t started winning yet, then keep at it and come back to this as you want to try a higher number of epidemic cards.
However, assuming that you have won the game a few times over and you want to try other strategies, here are a few I would suggest:
Control the disease; It’s a simple point, but you can quickly focus on building your hand towards curing the disease. However a cure is useless if the other diseases grow out of control by that point. To win on harder difficulties you will need to manage the balance between using cards to fly and using cards to cure. Specifically, I would suggest that each player focuses on one cure of a different colour – trading where necessary to make this happen. If you have the scientist in play, they may cure two or even three leaving one player able to roam and cover the gaps in controlling the disease
Build research centres; Early game research centres help you move and you will need to get to a research centre to develop the cure. However, consuming cards to do this can seem wasteful. Balancing the benefits and costs, will typically lead to building one research centre in each continent but no more – this is enough for travel and for quick cures, without too much cost (time and cards)
Always use the scientist; The scientist makes curing diseases much easier and allows the medic to roam (see below). However, if you are looking to up the difficulty without increasing the epidemic cards then take this player card out.
Mobile Medic; Again, it’s a trick you will already be using but really making sure your medic can focus on travelling and fighting the worst areas / the biggest outbreak risks will be core to winning. In particular, relieve the medic from searching for a cure as they will need the cards to travel and control the disease. This may also allow them to trade for others to cure.
Remember the cards; The biggest difference to winning and losing at the higher levels though is managing the epidemic cards. In particular when the epidemic occurs you shuffle back in the used disease cards on to the top. These disease cards are more likely to come back up. Focusing your efforts on these cities about to relapse and particularly those with the most disease cubes, will help you avoid a series of outbreaks in close succession. Sometimes it will be a tough choice and luck will go against you, but not remembering which cities are in that pile will make it impossible to balance your decisions.