Sickness is a process. It starts with some imbalance and develops as the body reacts to address the issue. Usually at that stage the system is focused on the problem and drives most of its energy to find a solution, which takes priority even over food digestion. Once the healing process advances, you start seeing the symptoms of the sickness, that are usually the signs of healing.
At that stage the body starts getting back to normal and needs to replenish its energy reserves. In order to replenish the energy reserves, eating more is required of course. Then you become hungry.