[PL 431] Utilitarianism and self-sacrifice

The justice objection to Utilitarianism goes like this:

Suppose a rape and murder [are] committed in a racially volatile community. As the sheriff of the town, you have spent a lifetime working for racial harmony. Now, just when your goal is being realized, this incident occurs. The crime is thought to be racially motivated, and a riot is about to break out that will very likely result in the death of several people and create long-lasting racial antagonism. You see that you could frame a derelict for the crime so that a trial will find him guilty and he will be executed. There is every reason to believe that a speedy trial and execution will head off the riot and save community harmony. Only you (and the real criminal, who will keep quiet about it) will know that an innocent man has been tried and executed. What is the morally right thing to do? The utilitarian seems committed to framing the derelict, but many would find this appalling" (Louis P. Pojman, How Should We Live? 2005).

One way in which a utilitarian can respond to this objection is by distinguishing between act-utilitarianism and rule-utilitarianism. According to the latter, it makes good utilitarian sense to have a principle of justice that members of a society generally adhere to.

Now, consider the following case:

Suppose that there is a new epidemic breakout. This new viral infection kills millions of people every day. Scientists have managed to isolate the virus and they are working frantically to develop a vaccine. In the meantime, you go to your doctor one day for a routine checkup. Your doctor draws blood from you and sends it to a lab for analysis. In the lab, the lab technicians see something unusual in your blood sample. They send the sample for further analysis, which reveals that you have a rare type of genetic mutation that gives you natural immunity to the new virus. Word about this spreads out rapidly, and soon after you are approached by public health officials who are asking you to donate more blood so that a vaccine can be developed from it. However, there is a catch. Since the epidemic is spreading rapidly, and people are dying by the millions every day, they need a very large sample of blood from you. In fact, they need all your blood in order to develop a vaccine quickly enough to save humanity. Basically, you have to sacrifice yourself for humanity's sake. What is the morally right thing to do?

In this case, it doesn't seem like the (rule)utilitarian can say that it makes good utilitarian sense to have a principle according to which one should sacrifice oneself for humanity's sake. What could a utilitarian say about this case?