@Tamirra.
The basic principles underpinning the development of vaccines have remained unchanged since the 1940s.Below is an approximation of what happens.
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1.Identify the virus to which you wish to create a vaccine.
2.Isolate and purify samples of the virus to add to eggs.
3.Add a seed quantity of the virus to millions of eggs, each of which act as viral manufacturing plants.
4.Once a sufficient incubation time has elapsed, process the eggs, extracting and purifying the newly grown virus.
5.Kill, attenuate or weaken the virus, to prevent the therapeutic dose administered causing the viral disease in the recipients.
6.Stabilise the virus, add bacteriostatic agents to prevent bacterial growth and contamination.
7.Dilute to appropriate levels consistent with a therapeutic dose.
8.Aliquot into vials, ready for administration by injection, or nasal spray.
Although the basic principles have remained unchanged, we have seen huge and significant improvements in our knowledge base, scientific understanding and manufacturing processes in the intervening 30 odd years since 1976.
A vaccine produced using modern manufacturing methods is a completely different product from one that was produced in the 1970s. Seed virus selection, purification methods, trace contaminant detection and removal, improved virus inactivation protocols, more comprehensive safety testing and clinical trialling make the vaccine markedly safer.
@Zac - not sure where you are getting your information from - All the sources I have consulted refer to a mass immunization programme against a swine flu like virus first noted in Fort Dix. This immunization programme took in around 25% of the US population before it was halted.