You can use either 'this' or 'that' in this sentence, depending on how close you feel to the situation.
We usually use 'this' when we are talking about something that is near to us, and 'that' when we are talking about something that is further away from us. However, there is no rule as to how close something must be to be referred to as 'this', or how far away something must be to be referred to as 'that'. In fact, the distance is best described as being relative distance.
For the purpose of knowing whether to use 'this' or 'that', distance does not have to be measured as 'physical distance' (i.e., the number of metres or feet), but we can also consider 'emotional or psychological distance' (i.e., how strong our feelings are to a person or thing, regardless of its physical distance from us).
In the case of the situation presented by the OP, emotional or psychological distance is more important a determiner of using 'this' or 'that' than would physical distance. If the speaker was William's mother, then she may use 'this' rather than 'that'. Her son's condition is something that she faces every day, and so she may feel that his situation is never far from her. If the speaker was William's teacher, then he/she may use 'that' rather than 'this'. William could be only one of several dozen pupils that he/she deals with in the course of a week, and she/he does not have to deal with the situation in the same way as William's mother.