Is it abuse to allow a bed bug infestation in your home?

My mom and her boyfriend have bed bugs, and have had them off and on for months. They buy the over the counter bed bug bombs, but they haven’t been working. I guess the boyfriend had them at his old house before moving to where they are now, so they’ve had them longer than I thought. I won’t let them baby sit my son over there, for obvious reasons. So my mom is pushing her boyfriend to get a professional to spray the house. He refuses because it’s “too expensive” but my mom knows a guy who will work for cheap, & he’s good, he’ll come back multiple times to spray for one payment. She used him when she had bedbugs a few years back & it worked. Her boyfriend refuses that too. He has three kids and they are ate up with bedbug bites, it’s miserable looking. I feel so bad for them. One of their teachers at school reported him to child services for abuse and neglect.

Is it abuse and neglect? If it’s been such an on going issue? My mom is offering to split the payment and get the treatment for the house but he won’t do it.