Influenza virus contains two highly variable envelope glycoproteins, hemagglutinin (HA) and neuraminidase (NA). The structure and properties of HA, which is responsible for binding the virus to the cell that is being infected, change significantly when the virus is transmitted from avian or swine species to humans. Here we focus first on the simpler problem of the much smaller human individual evolutionary amino acid mutational changes in NA, which cleaves sialic acid groups and is required for influenza virus replication. Our thermodynamic panorama shows that very small amino acid changes can be monitored very accurately across many historic (1945–2011) Uniprot and NCBI strains using hydropathicity scales to quantify the roughness of water film packages. Quantitative sequential analysis is most effective with the fractal differential hydropathicity scale based on protein self-organized criticality (SOC). Our analysis shows that large-scale vaccination programs have been responsible for a very large convergent reduction in common influenza severity in the last century. Hydropathic analysis is capable of interpreting and even predicting trends of functional changes in mutation prolific viruses directly from amino acid sequences alone. An engineered strain of NA1 is described which could well be significantly less virulent than current circulating strains.