She died of a disease called diptheria. This used to be a common disease, especially in children, before widespread immunization became available for it. Diptheria is a very contagious and potentially life-threatening infection that usually attacks the throat and nose. Early symptoms are a sore throat and mild fever. A membrane that forms over the throat and tonsils can make it hard to swallow. This membrane can also move deeper into the throat and block the airway, causing death.
All of Alice's children except Ella had it. Her youngest daughter, May, died of it. When her son found out, he was terribly sad and she kissed him to comfort him. And so she contracted it from him. She was already tired and worn out from taking care of all her sick children, so the disease killed her.