This relationship in which the heartworms gets nutrient from the host and in the process, the host eventually dies from infestation is known as parasitism.
The organism that houses the heartworm is called the host
The heartworm in itself is called the parasite.
Parasitism is a positive - negative relationship in which one organism feeds on the other and causes harm to it in the process.
Plasmodium falciparum is the parasite of malaria in man.
In commensalism, one organism depends on the other without causing harm to it. Example is cattle and egret.
Mutualism is a positive - positive relationship in which both organism derives benefits from the other. Example is lichen.
There are so many examples for that in different areas, like TPBi experiment carried out in our lab recently.Here's one link: http://www.alfa-chemistry.com/tpbi-cas-192198-85-9-item-282866.htm