Thank you for your query,
In children with sickness and disease, the appetite will decrease and followed by loss of weight due to decreased oral intake and catabolic state occurs with the disease process.
But as they recover from the illness, thier appetite will regain and they catch up the growth if the appropriate, nutritious diet is given.
Whatever the food served for your family that can be offered to him.
Try to give balanced diet containing all components of food pyramid and you can take a diet plan
from a dietician.
As your child is having there are chances of getting repeated cold and cough due to predisposition to allergic and seasonal response of the airways to the allergens.
Hemay need control and prophylactic drugs for asthma
or inhalational steroid
and bronchodilators depending on his severity.
So consult your Pediatrician
for the proper suitable plan for his asthma.
Hope I have answered your query.