“If it should prove correct that there were three strains of the influenzal virus, each with a periodicity of about 33 weeks, and that simultaneously all three strains became enhanced in both virulence and infectivity, then we are faced with a phenomenon without an exact parallel, although the behavior of the meningococcal viruses during the war presents some points of similarity. So far the weight of evidence leans to such an exaltation of a widespread endemic strain or strains rather than to dissemination from any particular focus in the world. In any case doubtless a good deal of spread of infection took place.”
Spear takes exception to the work of Brownlee and Stallybrass, and points out that the periodogram is not applicable to the study of recurrent epidemics unless the recurring waves are of approximately uniform “amplitude.” In that case nothing could be less appropriate for this study than the influenza waves which vary from very small to extremely high, as in 1918.
Spear describes two simple tests which he applied to demonstrate the existence or non-existence of periodicity.
First he divided each of the last thirty years into 13 four-weekly periods, and tabulated the frequency with which the observed week of maximum mortality falls into one or other of the 13 groups. He discovered that the climax of an influenza prevalence falls more frequently in the second and third four-weekly period than in others—i.e., the months of February and March. Had there been a 33-week periodicity there would have been an equal number of these climaxes in each of the 13 divisions of the year.
Brownlee, according to Spear, was correct in his prediction that influenza would occur in February, 1920, for the reason that January or February is the most likely time for an influenza prevalence in any year.
Spear’s second test of periodicity consisted in plotting the interepidemic periods according to the number of weeks intervening. Were there a 33-week periodicity, he says, that nearly all interepidemic periods should fall in this group. As a matter of fact, more than twice as many periods fall in the 42–58 weeks interval than in any other interval. Fifteen fall within this period, six in the period 59–75 weeks, five in the period 8–24 weeks, and only four in the period 25–41 weeks. There was one in the period 76–92 and one 110 plus. Finally in the thirty years 1890–1919 there were thirty-two climaxes or peaks in the “influenza” mortality.
Spear concludes that if there is any periodicity it is around fifty weeks, or a year.
The fallacy in the work of Stallybrass and of Brownlee, according to him, is that the mortality in the third week of 1892, the twentieth week of 1891, and the tenth week of 1895, and in the big epidemic of 1918 so overshadowed all the other peaks that the smaller ones became lost in these larger waves.
Brownlee does not claim a 33-week periodicity during interepidemic periods. This part of Spear’s criticism is not valid.
Vaughan’s objections to the conclusions on measles hold equally well with regard to influenza. Finally, we must remember that in parts, at least, of the work of Brownlee and Stallybrass, they are not studying chiefly influenza deaths, but deaths reported as due to bronchitis and pneumonia.