Periodicity.
The phenomenon of occurrence of epidemic influenza in many countries, even on different continents almost simultaneously and often without any clearcut progressive spread from one of these countries to another raises the question of periodicity in influenza. Is this simultaneous occurrence due to some mechanism in the life cycle of the influenza virus whereby it regularly acquires increased invasiveness, no matter what its geographical distribution, or is it merely a feature of the meteorologic conditions that makes the epidemic appear to be simultaneous in widely scattered communities?
Influenza characteristically returns. An influenza period usually comprises from three to five years, with one or two very mild epidemics at the beginning which may frequently be overlooked, then of wide pandemic spread, to be followed by endemic recurrences for as long as two or three years. During these influenza periods the intervals between waves are frequently so nearly equal or multiples of each other as to force the question of a periodic law. Not only thus, but even on a larger scale does the disease appear with a certain uniform regularity. The great epidemics are separated frequently by intervals approximating decades. Stallybrass calls attention to the epidemic years in England, which are 1789–90, 1802–03, 1830–32, 1840–41, 1848–49 and 1851, 1854, 1869–70, 1879, 1890–91, 1898, and 1918–19. With the exception of 1854 all of these dates are around the end of a decennium.
Yet, again, in the successive waves of an individual epidemic, as has been pointed out by Pearl, there is very roughly some periodicity.
Are these admittedly obvious phenomena fundamental features of the life cycle of the influenza virus, or are they incidental, due to extrinsic causes, changes in the pabulum, in the host as an individual, or in the host as a community, or changes in climatic conditions? Is it a basic feature upon which we must build our conception of the epidemiology of epidemic influenza, or is it more a feature of chance? The evidence to date is conflicting and incomplete. The answer lies in the future.
Periodicity in the acute infections is not a new subject. It has been discussed in various other diseases, particularly in measles. For many years epidemiologists in many parts of the world have reported the observation of a periodicity in epidemics of measles. It is generally regarded as an established fact that each locality suffers from epidemic waves of this disease and that the period is somewhere about two years. In certain relatively small localities in England where registration statistics have been kept for many years the Health Officers count on an epidemic every two years. In some places the epidemic is expected to fall during the even years, while in others it occurs in the odd years.
Brownlee has been one of the foremost investigators in the periodicity of influenza, but since his communication on that subject was very brief, we take occasion to quote first from his article on the periodicity of measles, thereby gaining a more comprehensive knowledge of his theory, and at the same time becoming able to compare the periodicity in the two diseases.
“The common explanation of the periodicity of epidemics of children’s diseases is that the susceptible children take the disease in sufficient numbers to limit the further spread. The epidemic thus dies out to recur when a further sufficient number of susceptible children have accumulated. This is quite a feasible theory and certainly explains the periodicity of epidemics. The forms of epidemic curve which arise on this hypothesis are not unlike those actually found, the differences being no more than might be expected between a mathematical form based on a hypothesis and the natural conditions to which the hypothesis is only an approximation. This explanation, however, must fail if epidemics of different periods can be shown to exist in the same town at the same time, and I think this has been shown. In London, which on account of its size might be assumed deserving of special treatment, the existence of periods of different length have been demonstrated. In Edinburgh, Glasgow, and Birmingham also it has been shown that epidemics with periods in the neighborhood of ninety-eight weeks and one hundred and ten weeks intermix. The same epidemicity even applies to districts in London. In the West end of London we have almost a replica of what occurs in Glasgow, Birmingham and Edinburgh. The main period there is 97 weeks, the secondary period 109.5 weeks. In the South of London one period is that of 97 weeks, but almost equally prominent is that of 87 weeks. The whole evidence, therefore, seems to point to some condition in the organism which produces the disease as the potent cause of the difference rather than to the number of susceptible children. Compare the Paramoecium which under natural conditions divides asexually for several hundred times and then dies out unless conjugation takes place. The resting stage following conjugation persists for some time.
“There is, however, one point of great importance which must be considered. If an epidemic begin in a definite locality and spread from that locality, and if there is no loss of infectivity on the part of the organism, it is demonstrable that a similar proportion of the population should be attacked in each zone as the epidemic spreads outward. On the other hand, if the organism lose the power of infecting with the lapse of time, in each additional zone invaded the proportion of susceptible persons infected should become smaller and smaller. Of course this might not be true for any one epidemic, as in many parts of the area invaded the population might be more or less susceptible because of recent attack of the disease, but when an average of twenty outbreaks has been taken this effect should be eliminated, the number of times the invading organism comes into contact with an insusceptible population being balanced by the number of times which it meets one more susceptible than the average. The method of spread of epidemics on the average should thus give some indication regarding the laws which determine the course of the phenomenon. Now with regard to London, the clearest facts refer to the 87-weeks, the 97-weeks and the 109.5-weeks period. The 97-weeks period starts at the same time all over the city and there is no evidence of any special center. The infection seems generalized. With regard to the 87-weeks epidemic, however, the case is different. This seems to start in St. Saviour’s Parish and to spread thence to Camberwell, Lambeth, etc. In this epidemic the rate of spread can be definitely measured. The maximum occurs later and later as the distance from the center is increased and the percentage of children infected is also easily observed to fall as the time increases. With regard to the 109.5 weeks’ period epidemic the facts are similar though not quite so definite. This seems to show that for at least two strains of organisms the epidemic ceases because the organism has lost its power of infecting. It may be inferred that an epidemic ceases because the organism varies in its potency to cause infection. A cycle of epidemics now coinciding and now differing in their maxima can thus be explained. Some kind of life cycle exists in the infecting organism. In this life cycle high powers of infecting are attained probably after a resting state: a period of activity follows and gives place to a period of rest; the average length of the cycle is determined by the strain of the organism.”
There are certain drawbacks to Brownlee’s work and conclusions. We quote from V. C. Vaughan, who has discussed Brownlee’s work, not only because of his good summary of the difficulties and disadvantages of the method, but particularly because the same disadvantages and possibility of inaccurate conclusions hold in the case of influenza.
“There is no reason for supposing that the virus of measles is controlled in any way by our calendar. In order to get anywhere in determining any law of periodicity in epidemics we must know the morbidity and mortality of the disease by days, or at least by weeks. In different parts of a large city there may be, and undoubtedly are, epidemic waves of measles on the flow or on the ebb at the same time. The best work that has been done along this line is that of Brownlee, who has figured out epidemic waves of measles, based on the weekly numbers of deaths in London between 1840 and 1912.
“The figures presented by Brownlee are of great value, and his theory is fascinating and has much in its favor, not only in a study of epidemics of measles, but of the other infectious diseases of infancy and childhood, especially scarlet fever, whooping cough, and chicken-pox. In order to solve the problem of periodicity in measles we must have more exact information than we now possess. Brownlee’s figures pertain to deaths only. There are, so far as we know, nowhere in the world satisfactory statistics concerning morbidity in this disease. Deaths from measles are so largely determined by the care bestowed upon the sick and upon the extent to which secondary infection is prevented that we are inclined to hesitate about the acceptance of a death rate or number of deaths from this disease as an index to the virulence of the organism causing the disease; in other words, we are not convinced that the death rate in a given outbreak of this disease is a measure of the virulence of the organism causing it. This involves the question whether measles per se is a disease of wide variation in malignancy or are the widely different death rates observed in different epidemics due to secondary infections. The streptococcus, a common invader of the body during the progress of a measles infection, is known to possess a most variable degree of malignancy. We are inclined to the opinion that if all cases of measles could be recognized before secondary infection occurs and could be cared for ideally the death rate from this disease in different epidemics would be much more uniform than is now shown and would be low. The greatest danger to life in an attack of measles lies in the fact that the virus lowers the resistance of the body cells and opens gateways to more deadly organisms, such as the streptococcus. We believe that there are demonstrated facts which support these ideas. Quite uniformly in measles there is a well marked leukopenia. As we now interpret it, this means a decrease in the number of the forces that naturally protect the body against the invasion of foreign cells. Again as we interpret it, the failure of the body cells to respond to the tuberculin test during a course of measles or soon thereafter is evidence that the resistance of the body is lowered. If our interpretation on these points be correct we fail to see how deaths from measles can be properly employed as a standard in the measurement of the virulence of the organism of the disease.”
Recognizing then the obvious disadvantages of the method, we will turn to the work done on periodicity in influenza. We should call attention at this point to the fact that the establishment of periodicity would carry with it the assumption that the third of our three hypotheses concerning the origin of influenza is the correct one. For example, the July and autumn epidemic in England, as well as all occurring subsequent to them, would be due to a virus or several viruses which have been endemic in England since 1889, in fact since man has been in England, and the epidemics and their recurrences would be due to increase in the virulence of this local virus. The virus is distributed over the earth and may become virulent periodically in many countries at the same time, or if the periodicity is different on two continents the epidemics would occur at different times.
Periodicity is not a new hypothesis. Hirsch denied any periodicity distinct enough to be revealed by the comparatively crude statistical methods of his time. Periodicity if present can only be revealed by detailed and complicated mathematical procedures. Brownlee has investigated the weekly number of deaths from influenza in London between 1889 and 1896, and also up to the present time. He has compared these with the weekly number of deaths from bronchitis and pneumonia in London, the records of which have been available since 1870. By the method of the periodogram he showed that there was a regular periodicity of 33 weeks in deaths from influenza between the years 1889 and 1896, but that in later years there was some considerable aberration. He concluded that for some reason influenza periods tend to recur at 33-week intervals after the primary epidemic, and that the favorable season for its recurrence is from January to the end of May. Should the 33d week fall in other than these winter months the epidemic may be mild or even missed, appearing after another 33-week interval. Epidemic influenza does not assume a form which causes any large number of deaths until a bronchitic or pneumonic constitution has been established. The fatal form is usually a disease of the winter or spring. He also found that in the absence of influenza, bronchitis and pneumonia did not show a 33-week periodicity, but when associated with influenza these conditions also became periodic (33 weeks), and he assumes that this change is definitely associated with the appearance of influenza.
Between 1876 and 1890 there was no tendency to the 33-week periodicity with regard to bronchitis and pneumonia, but it was very marked between 1889 and 1896. During this epidemic period the deaths from pneumonia precede those from influenza by one week and those of bronchitis precede those of influenza by two weeks. The number of deaths from bronchitis and pneumonia ascertained by this method of grouping is fully twice the number obtained from influenza alone.
He believes that in these years, influenza appeared, on its epidemic onset, first with bronchitic symptoms, later with pneumonic symptoms, and lastly with those symptoms more definitely associated with influenza proper. When the several sets of deaths are added together in 33-week periods a very typical epidemic makes its appearance.
Brownlee finds that in the monthly statistics of Glasgow, Aberdeen, Massachusetts, etc., there has been nothing differing essentially from this phenomenon found in London.
Between 1876 and 1889 the annual curve for bronchitis and pneumonia shows two maxima, one at the end of January and the second in the middle of March. From March the decline in deaths from bronchitis is very rapid. The disease re-appears around the beginning of October. During the period 1889–96 the maximum number of deaths from bronchitis occurred in the second week of January and the last week of February. Both of these maxima are a fortnight before the maxima of the epidemics of influenza. This suggests that the advent of influenza has brought a change in the seasonal prevalence of bronchitis and supports the view that the earlier portion of the influenza epidemic is associated with bronchitic symptoms. The same phenomenon holds for pneumonia.
Brownlee was able to predict correctly the date of the recent 1920 epidemic. He did not attempt, however, to explain the short interval between the summer and autumn, 1918, epidemics in England. He speaks of the second as “aberrant.” In other words, it does not fall within his classification. October is not a high respiratory disease month. The epidemic should have been mild.
Stallybrass has confirmed Brownlee’s 33-week periodicity and suggests an explanation for the “aberrant” October epidemic. Using periodograms with a 33-week basis, and plotting deaths from influenza and respiratory diseases from January, 1890, through January, 1920, he finds that the most definite 33-week periodicity is shown during the years 1890–99. During this period there is one maximum, when all 33-week periods are superimposed, which occurs at the seventh week of the cycle. Beginning about 1899 a new maximum appears in the nineteenth week of the cycle, which continues to recur until the culminating point is reached in the week ending October 26, 1918. An additional 66 weeks carries the date forward to the first week in February, 1920. The maximum at the seventh week of the periodogram during the years 1899–1913 is greatly diminished from that in 1890–98. The periodogram for 1914–1919 shows clearly both maxima, that in the seventh and that in the nineteenth weeks.
We quote Stallybrass in some detail (see Chart XII):
“Dr. John Brownlee pointed out that from July 13th to March 1st (the maxima of the summer wave of 1918 and of the spring wave of 1919) is 33 weeks, but that the wave having its crest in this country on November 2, 1918, does not fall into the sequence, leaving one to infer that there were two strains of the influenzal virus in operation.
“I supplement his investigation by the weekly deaths occurring in Liverpool during the period 1890–1919 that were ascribed to influenza and to all respiratory diseases. Prior to 1890 there were no deaths attributed to influenza for a number of years.
“Closely corresponding with Brownlee’s observations on London by far the most definite periodicity is shown during the years 1890–1899, during which period there is one well marked maximumly at the seventh week of the cycle. During the period 1899–1913 a new maximum in the nineteenth week of the cycle comes into play and continues to recur until the culminating point is reached in the week ending October 26, 1918, a week earlier than in most English towns (Wave III); a further 66 weeks carries one forward to the first week in February of this year, as Brownlee pointed out, and the outbreaks that are being reported in Japan, Paris, Chicago, New York, etc., would show that this strain has punctually reappeared.
“There is also evidence in the table of a small maximum at the twenty-seventh week of the cycle in the earlier sub-period, and at the twenty-ninth week in the later sub-period; slight movements of the maxima forwards or backwards in the cycle over a number of years may, perhaps, indicate a periodicity slightly greater or less than 33 weeks. The twenty-ninth week of the cycle fell on the weeks ending May 18, 1918, and January 10, 1919. An examination of the figures in Dr. Hope’s annual report for Liverpool for 1918 shows that there was a definite wave of influenza reaching its crest on May 18th (Wave I), and there is also a definite rise in the deaths from influenza, respiratory diseases, and from all causes, making a small peak in the week ending January 3, 1919, but it is hidden by the enormous waves of October and March, so that it only appears as an irregularity in the curve; but it was noted at the time that influenza had not declined in Liverpool in January in the way that it had in practically all other English towns. These two waves do not appear to have played a large part in this country, but the outbreaks in the Grand Fleet in May, 1918, and also in Spain, Glasgow, etc., may, perhaps, be attributed to it. In the United States in January, 1919, it would appear to have played a much larger part. In a large number of American cities two waves are experienced, the first being the October wave; the crest of the second wave sometimes fell in March, as did one of the crests in this country, but in a number of instances, e.g., Cambridge, Washington, San Francisco, New Orleans, etc., it fell in January, or to be exact, in the thirty-first and thirty-second weeks of the cycle. The close relationship of Liverpool and Glasgow with the United States through the incoming stream of American troops may perhaps account for the presence of this May wave in these two towns, and not the rest of England.
CHART XII.
Periodogram based on the weekly influenza deaths in Liverpool between 1890 and 1919. The curves are based on a thirty-three week periodicity. (Stallybrass.)
“The third maximum in the fourth week of the cycle is represented during the late outbreak by the waves culminating in Liverpool, and also the greater number of English towns on the weeks ending July 13 (Wave II) and March 1 (Wave IV). This is a 33-week interval. This wave recurred at an interval of 32–34 weeks in a large number of English towns.
“Of 65 towns which experienced all three waves 47 (72 per cent.) had their maxima in the summer and spring epidemics within an interval of 32–34 weeks; but comparing the week in which any given town had its epidemic peak in the summer and autumn, and autumn and spring epidemics only 27 (41 per cent.) and 31 (47 per cent.) respectively fell within the limit of a week on either side. The time relationships of the maxima in summer and spring were much closer to each other than they were to the autumn maxima.
“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.
After a study of the pros and cons of the question of periodicity the author submits by way of summary his conclusions:
1. Influenza does tend to recur at intervals. It has not been proven that these intervals are always of equal length.
2. At the present the opinions concerning the periods are divergent. We have the 33-week periodicity of Brownlee and Stallybrass, the one-year period of Spear, the seven-week intervals suggested by Pearl, and the apparent twelve-week recurrences in England in 1918 and 1919.
3. It is to be noted that particularly in the work of Stallybrass, in order to prove his periodicity, he finds it necessary at times to quote epidemics occurring, not in England, but in fairly remote parts of the world, as in the United States and Japan. We have shown that in the interval between 1918 and 1920 an epidemic could be discovered somewhere on the earth in many months, perhaps even in every month during this interval. It is to be regretted that following the criticism by Spear there has been no further report, so far as we know, by either Brownlee or Stallybrass.
4. It is quite possible, even probable, that influenza is endemic in mild form throughout the interpandemic years in England, as well as in many, or all other countries, but it is equally possible or probable that the particular virus which gave rise to the pandemic was not one which simultaneously increased in virulence in all countries, but was one which had its origin in one comparatively well localized focus.
5. Our own theory does not explain the autumn recurrence in 1918 in England, following that of May, June and July. We have traced the original spread to England and have left it at that point. We have again taken it up in the autumn when it became severe, and was returned to the United States. The interval of quiescence in England and elsewhere may need further explanation. Two alternative hypotheses suggest themselves: First, that the autumn recrudescence is entirely comparable to later ones, and is but a manifestation of the characteristic feature of recurrence in influenza. Had the autumn epidemic been mild and had it not so overshadowed all others, we would have classified it with those of early 1919 as being merely recrudescences of the summer spread. Evidence, particularly in favor of this, is the report of Greenwood previously mentioned which shows that in England the autumn spread partook of the nature of a secondary type of epidemic, as compared with the primary type in the summer.
The second hypothesis is that the occurrence in the summer in England of an epidemic due to a virus imported from America or France or China, with its consequent increase in morbidity, so enhanced the virulence of a local endemic British virus that the latter produced the autumn epidemic. We see no necessity for complicating the question by the assumption of this second hypothesis.
6. Whether or not there is a regular periodicity of a definite number of weeks in the case of influenza, the fact remains beyond cavil that one of the dominant characteristics of epidemic influenza is its recurrence at intervals. The evidence is ample that the disease is distributed throughout many countries in interepidemic times and that intermittent outbreaks of large or small extent occur.
The most striking phenomenon is the fact that in March of 1918 influenza is reported as having been present in China, in the United States and in France. It is scarcely possible that the disease in its epidemic form could have been carried from any one of these three points to the other two in the remarkably short time between the onset of the three outbreaks. We are faced with the phenomenon of a simultaneous exaltation of the influenza virus in three remotely separated countries of the world. This one fact more than any other indicates that the fluctuation in virulence is dependent upon some factor intrinsic in the virus itself and not upon environmental factors.
It is impossible at the present time to decide whether the world epidemic spread simultaneously from these three foci or whether in only one of these three the virus became so exalted as to produce pandemic prevalence. All we can say is that we are able to trace consecutively the spread of the influenza from the focus in the United States throughout the world. The information upon which we base our findings is not statistical, and as we have previously said this latter type of demographic study should be brought into use to either corroborate or disprove our findings.