I’ve often noticed people saying this. Considering all the rapidly appearing SARS-CoV-2 mutations we've seen, it's easy to think this. But it's not quite correct. It's enough to make me launch into yet another virology lecture.
What’s different about influenza? Why is it that there is a new influenza vaccine every year, yet we have the same polio, or measles-mumps-rubella (MMR) vaccines year after year? How does SARS-CoV-2 fit in to this?
Influenza A viruses each contain eight different strands of RNA (called viral ribonucleoprotein complexes (vRNPs). Each RNA strand encodes different viral genes. A functional influenza virus particle must have all eight vRNPs. These eight strands of RNA are important, and I’ll come back to this later.
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Here’s a schematic diagram of Influenza A virus structure. The envelope of the virus particle contains three trans-membrane proteins. Two of these surface proteins are called hemagglutinin (HA, or H) and neuraminidase (NA, or N). They are important because these proteins are most often recognized by our immune system, as a result of infection or vaccination. (Other proteins encoded by the virus genome: M1, M2, PB1, PB2, PA, NS1, and NS2/NEP, are shown in the diagram, but I won’t mention them further.)
Different Influenza A viruses encode for different HA and NA proteins. For example, the H5N1 virus designates a subtype that has a type 5 HA protein and a type 1 NA protein. There are 18 known types of hemagglutinin and 11 known types of neuraminidase, so, in theory, 198 different combinations of these proteins are possible.
During influenza infections, it is common to have more than one strain at a time in an infected person or animal. During virus replication, the eight RNA strands from these different strains can easily mix. As long as the new virus particles have a copy of eight strands, it doesn’t matter which strains they came from. As a result, new strains can easily appear, with new combinations of HA and NA.
Each year when new Influenza A vaccines are made, the world’s virologists have to decide which strains are coming next. They don’t choose only one strain. Usually 3 or 4 likely candidates are picked, and they develop vaccines against each. When you get a flu shot, it contains a mixture of these. As you can easily guess, some years this can lead to more effective vaccines, and other years, the vaccines are less effective.
In contrast to Influenza viruses, coronaviruses, such as SARS-CoV-2, have only one larger RNA strand. All its essential genes are coded by this one strand. See RNA genome in the diagram below.
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When these viruses replicate the new virus particle must have a copy of the single RNA genome. Yes, many mutations do occur, but coronavirus don’t have the eight strands that Influenza A has, along with it ability to trade strands during mixed infections.
I condensed information and took the diagrams from three different Wikipedia pages:
https://en.wikipedia.org/wiki/Influenza_A_virus
https://en.wikipedia.org/wiki/Orthomyxoviridae
https://en.wikipedia.org/wiki/Severe_acute_respiratory_syndrome_coronavirus_2