Herd immunity isn't "the truth". It's an emergent property of…

I put together a simulation for you, using Nicky Case's Emoji simulation engine. This should explain it. Click next to a group of unimmune people to vaccinate them.

Since the simulation is so small, I put in an unsafe, mostly-effective vaccine; you will see the vaccine making people ill, to a much greater extent than happens in real life. (Orders of magnitude of a higher extent.) The illness is also pretty fatal, but not too fatal to spread to literally everyone in the simulation.

Feel free to share it with other people, if you find it helpful. The code's a bit hackish and sporadic (you can see it by removing the "edit" parameter).