Can we find a vaccine for every strain?

Finding a vaccine for every single strain or a "universal" vaccine that does not need changing every year is quite a difficult task as there are an unknown number of different strains but it could potentially wipe out Influenza altogether. This area is getting more and more attention from pharmaceutical companies and it seems that it could be quite possible in the near future.

Types of Influenza and the number of subspecies
There are 3 types of influenza: Influenzavirus A, B and C.
Influenza A virus is the most dangerous type to humans; it is the most common, most infectious, most deadly and evolves and mutates the fastest. Because of this last fact it has the highest number of different strains and can infect humans, birds, pigs and other animals. Type A causes both seasonal Influenza and Influenza pandemics. There is an unknown number of Type A subspecies but there is around ten that are quite common and dangerous in humans. The deadliest subspecies is H1N1, which caused both the Spanish Flu Pandemic and the Swine Flu Pandemic.
Type B is much more stable than Type A. It is only found in humans and only has one subspecies. Type B mutates a lot slower than Type A and so it much easier to have a resistance to it. However it still evolves enough for immunity not to last. Type B cannot transmit from one animal species to another and so antigenic shift does not happen and this means that Type B only causes seasonal Influenzas and never Influenza pandemics.
Type C infects humans, dogs and pigs. Type C has only one subspecies and is much less common than the other two types and usually only causes mild illness in young children.

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Influenza vaccinations
These days if you get an Influenza vaccination you get vaccinated for 2 Type A viruses (H1N1 and H3N2) and the Type B virus. This means you can still get Influenza even if you’ve been vaccinated. The strains are chosen because they are the most dangerous. The formula for Influenza vaccines needs to change each year to keep up with the viruses’ mutation rate.
The idea of a universal vaccine is that one vaccine would not need to change, and would give immunity to all the different strains. Vaccines at the moment mainly focus on developing antibodies that attack the antigens on the virus. However there is a different way of attack being developed at the moment that attacks the stems of the haemagglutinin (an antigen). The stems of the antigens mutate and change a lot less than the antigens themselves. A vaccine that targeted the stems would not need to be changed as often as vaccines these days and be a huge step forward in curing Influenza.