The fact that people don't volunteer doesn't mean that they don't care. Probably they would welcome the opportunity to visit-if they were asked. I'm afraid I'll be turned down if I invite people or if I ask to visit them. This way you are not so personally involved. If you ask people to do something they enjoy doing, it is more likely that they will accept.
Some people feel awkward talking to someone who is sick.
They don't know what to say. Then they can talk about what they are doing, or they can be comfortable not talking at all because they are paying attention to what they are doing. The person I am caring for says he doesn't want people to see him when he is sick. Encourage talking to people on the phone. You may also suggest inviting people who are used to seeing sick people-for example, people who have been caring for someone who is sick.