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That person will come into contact with people who cannot be safely vaccinated (those with compromised immune systems, young, elderly etc) who are most at risk for the diseases. And as such the person can be a carrier.
Everyone who can be vaccinated should be vaccinated to maintain Herd Immunity
The way vaccines work is mainly through herd immunity. No vaccine is 100% effective, but if the people around someone who is infected are vaccinated, the chance of it spreading to others is minimized. This is what stops epidemics before they happen.
They are risking contributing to the cause of such an epidemic. It could be avoided in the first place by people being responsible with their health and getting vaccinated to begin with.
If I consider an unvaccinated person a threat to my body, then I am ethically justified to protect myself against the threat by, for example, excluding the person or discriminating against them.
This compromises people who are heavily at risk, such as people with AIDS, the elderly, and the very young. Because relationship webs grow exponentially, there is a sharp rise in cases even during a small decrease in vaccination rate.
This decision doesn't just involve himself, he's putting a lot of other lives at risk. The anti vaccine argument is nothing but ignorant. People don't have the right to make decision that put other people at risk. If I have Ebola, I don't have the right to just walk out the hospital.
That could also expand the epidemic, if they refuse vaccination they should have to be isolated as to assure no further spread, especially with a viral infection.
Forcing vaccination reduces individual liberty, which constitutes a form of diversity with evolutionary and ecosystem implications. This reduces the agility of the system to withstand poor decisions. A vaccination that turns bad could kill a high percentage of people. Imposed vaccination? 100%.
Regardless of a persons reasons for not wanting vaccination, the actual risk to those around them is not high enough to warrant the forcing of a medical procedure on an individual.