The pathogen has had 4 days to spread after the initial infection, and 4 people have been vaccinated.

Just like in the first puzzle, because there are not enough vaccinated people to stop the pathogen at every edge of the contact chart, at least some of the people at the edge will have been infected on the fourth and final day.

Let's start by trying to align those people along the bottom left edge and working backwards towards the center of the infected population. (Note that the dotted line in each chart connects other possible patient zeros, with preference given to those nearest the center of the chart.)

Filling out the rest of the chart, this requires 6 vaccinated people to explain the infected population, and there are two people who are not infected until the fifth day.

Instead of choosing the central possibility for patient zero, let's try picking the one further to the right in the contact chart.

Again, this requires 6 vaccinated people, but now there are three people who are not infected until the fifth day.

Notice that in both of these scenarios, everyone in the top-left or bottom-right corners of the chart are either 3 or 5 contact days away from patient zero, instead of the required 4. This suggests that we should try aligning people infected on the fourth at the top-left (or bottom-right) corners.

Now the number of vaccinated people is down to 4, although there are still several people that would be infected after the fourth day.

But there is another possible option.

By moving patient zero down and to the left, those patients at the bottom of the contact chart are infected by the fourth day, and this still only requires 4 people to be vaccinated.