The person with apathy may be totally disinterested in activities preferring to sit doing nothing for hours. This can be mistaken for depression but if the person is apathetic they may not have any feelings of sadness or low mood. They may appear to be content to sit as the world goes on around them.
The best way to help to overcome this apathy state is to encourage normal activity and to stimulate the brain with activity. Walking, exercise and physical tasks within the persons limitations should help. In the same way that the brain makes new pathways and connections for physical tasks, it may be possible to do the same for behavioural issues. Even if the person has limited physical ability you could still take them out in a wheelchair. Try to do chair based exercise as recommended by a physiotherapist or meet others socially to encourage interaction.