Measles

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Travelling waves and spatial hierarchies in measles epidemics – Grenfell, Bjornstad
https://www.researchgate.net/publication/11615103_Travelling_waves_and_spatial_hierarchies_in_measles_epidemics

This paper from epidemiologist Bryan Grenfell shows some very interesting features in the epidemiology of measles, A ‘wavelet’ model is created that characterises the UK data as a series of wave-packets that originate from the large cities and spread out over the rest of the country,

Further computer modelling shows how various features of the wave model can be explained by human-to-human transmission driven by population dynamics and seasonal forcing.

The wave patterns are quite surprising, are not obviously connected to the seasons and are not consistent with the idea that measles is the immediate result of a poisoning event.

This paper is a good example of why mathematical modelling is sometimes necessary and how it can give insights into the underlying structure of noisy data.

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London measles cases 1944 – 2000

The chart shows the “Wavelet time series analysis for the log-transformed weekly London measles time series” – so the data has already been manipulated somehow.

Several interesting and surprising features are immediately apparent.

The chart starts with an apparent seasonal variation which, by 1950, has transformed into a biennial pattern with strong peaks every two years and a ‘mini’ peak in between the main peaks. The peaks are very well defined.

After 1970 the absolute number of cases declines and the biennial pattern degenerates into just ‘noise’.

Varying time period

Somewhat surprisingly for such a sharply defined pattern, the period is not actually tied to the seasons and is not precisely biennial. Instead, mathematical analysis suggests a period of slightly larger than two years that, even so, varies as time progresses; see the blue line below.

The red line shows the onset of vaccination programs and this is assumed to somehow affect the biennial rhythm.

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Phase differences between cities

The modified data from three cities, London, Norwich and Lincoln are plotted on the same chart and we immediately see that measles in the three cities peaks in different years and at different times of the year.

In addition to this, the blue peaks (Lincoln), at first out of step with the other cities, are perfectly synchronised by 1990.

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Modelling the data as a flexible wave function

Data such as the above are not expressible as a single mathematical equation and so are not amenable to statistical analysis. What is needed is a further abstraction of the data in order to somehow obtain a quantitative analysis of these phenomena.

The illustration below shows (top chart) the data modelled as a set of ‘flexible’ waves and we can now clearly see a striking pattern, that of three wave functions having no initial phase relation gradually and smoothly attaining a perfect synchrony.

Note that in 1951 the black and red have perfect phase-alignment with each other but are completely in opposition to the blue line of Norwich.

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The bottom chart shows the calculated phase difference between Cambridge and Norwich and between Cambridge and London. The averages are non-zero and differ from each other but eventually achieve synchrony in 1962 before starting to diverge again.

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Spreading from major cities

The illustration shows the phase difference of disease incidence relative to London.

Measles outbreaks that start in London will radiate outwards from the capital city at a rate of about 5km per week, with the rate of travel depending upon local population densities. The pattern is clear for a radius of about 30km around London with ‘randomness’ in rural areas eventually dominating.

Similar ‘spreading’ patterns exist with all the major cities with things being less clear in the North-East where the proximity of several large cities leads to interference patterns in the spreading waves.

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A transmission model

Grenfell does not make the claim that these data prove contagion, rather contagion is assumed and the task of the paper is to try to explain the characteristics of the data in terms of transmission parameters.

• Measles epidemics are self-limiting and will subside when all ‘susceptibles’ (children) gain immunity
• ‘Extinction’ events occur in rural areas when the disease dies out for lack of new victims
• Disease remains ‘endemic’ in larger cities and replenishes the surroundings with virus on an approximately biennial basis when there are enough new children
• What is effectively random transmission between individuals will form stable attractor patterns at the population level and it is these that are manifest in the data
• Phase-locking between attractors along with seasonal forcing gives rise to synchrony between cities and an apparent underlying rhythm
• The decline of measles after the introduction of vaccine programs is assumed to be because of those vaccination programs

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Concerns and questions

Seasonal forcing

The stated importance of seasonal forcing seems at odds with the model which at no time shows a precise biennial pattern, which varies across time and is different for each city.

“Because epidemics do not suffer local extinction, and because all the cities experience the same seasonal forcing, no lags are generated.” – Grenfell

“The task is aided by epidemiological models, which capture both the nonlinear dynamics of childhood epidemics as a function of local population size and the impact of significant environmental forcing. This forcing mainly comprises seasonality in transmission, due to schooling patterns, and longer-term variations in susceptible recruitment, due to birth-rate variations and the onset of vaccination” – Grenfell et al

The saw-tooth shape of an epidemic

The paper concentrates on modelling epidemics as waves and therefore does not address the issue of the characteristic ‘saw-tooth’ shape of the epidemics.

Other authors have commented upon this with respect to influenza. We expect from an epidemic that the initial increase in cases is rapid and follows an exponential curve and that thereafter a rounded peak will be reached and a long decline will ensue. The tail end of the curve is expected to stretch out as the disease finds fewer and fewer people to infect.

What we see instead is a very sharp peak that is followed by a decline that is much faster than the initial rise in cases.

Extinction events

The virus is said to disappear from rural areas in between epidemics but to be replenished from the big cities in time for a new outbreak, meaning the survival of the virus depends upon the specific population densities and behaviours. The question then arises: “How did measles survive before modern population densities, primary schools and contemporary commuter habits?”

Measles is ‘endemic’ in large cities

“In the large town, measles is endemic throughout the interepidemic trough, so that a new epidemic occurs as soon as the effective reproductive ratio of infection exceeds unity; this threshold is determined by the accumulation of susceptible children, modified by seasonally varying transmission rates associated with the school year.

“By contrast, in the small town, infection goes extinct locally after an epidemic; therefore, another epidemic cannot happen until an infective `spark’ is received, generally originating in a larger (endemic) community.” – Grenfell

What does it mean to say that measles is ‘endemic’?

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Standard transmission models

The graph below shows the outcome of a basic epidemiological model.

Cases (red) initially show a rapid (exponential) increase in numbers as the infection spreads to more and more susceptible individuals. As the number of susceptible individuals reduces so the increase diminishes but still infections remain high as there are still plenty of ‘spreaders’ around.

As the number of spreaders starts to wane and the number of susceptibles continues to diminish, the curve takes a steeper downturn and infections decline rapidly.

In computer models such as this a long ‘tail’ is produced as, although new infections are declining rapidly, there is a large pool of infected individuals remaining.

This hides what is really happening which is that contact with an affected individual is becoming increasingly and rapidly unlikely. Take a look at the number of susceptibles; it declines rapidly as soon as the epidemic starts and reaches almost zero even whilst cases are still near their peak.

We have, at peak number of infections, only 0.2 infected people per 1000 which means 2 cases per 10,000 – and the disease is still being passed on somehow!

Even so, the model is assuming a perfect mixing of the population and within this model there is always a non zero probability of a sick person making a transmission to a healthy. In practice I think this would not be the case and that instead there would be a very sharp decline in new cases once the proportion of infected individuals reached some threshold, below which transmission simply did not occur.

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‘Non-epidemic’ activity

This then is a glaring weakness in the transmission theory, that the number of susceptible individuals decreases to almost zero during an epidemic and yet must somehow remain above zero for another two years to spark off the next epidemic.

A spreading virus is only able to stay alive by actually spreading and once the effective reproduction rate is below one, it is declining rapidly.

To make any sense of this, modellers must somehow keep the virus alive and yet not spreading during interim periods and so will add some other mode of survival to allow for this:

“We then fit a seasonal regression model to the truncated series to estimate the expected baseline number of deaths in the absence of epidemic activity. A nonepidemic threshold was defined by the upper limit of the 95% confidence interval derived from the seasonal regression model. Only influenza activities that remained above the threshold for >2 consecutive weeks were included in the analysis” – Viboud et al

So there is now something called ‘non-epidemic’ activity for influenza which keeps the virus alive somehow even though there is no measurable spread. In the case of measles, lifetime immunity is claimed which further reduces the possibility of spread in between epidemics.

Without this ‘fix’ to the models there would surely be very many extinction events even in population dense areas.

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The decline in measles

The chart shows measles deaths from 1900 to 1960. A strong rhythmic pattern with a period of about 3 years is seen, along with a marked decline, almost to the point of extinction, before vaccines were introduced after 1960.

The vaccines therefore cannot be the cause of the decline in deaths.

Note that these data are averaged over a whole nation so we don’t have the geographical refinement of the Grenfell paper but if we take all these results at face value we have a disease showing an approximate three year cycle that, as global incidence declines, diminishes to a two year cycle, followed by a one year cycle and eventual disintegration of structure into mere ‘noise’.

What produces this? Do Bruce Grenfell’s attractor patterns extend to the whole of the United States as well?

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Modern measles age distribution

The chart below from Muscat et al suggests that measles can no longer be considered a disease of childhood.

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Seasonality

Measles is seasonal in many countries particularly in the spring:

Modelling seasonal measles transmission in China – Bai, Liu

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Measles and the weather

The effects of weather conditions on measles incidence in Guangzhou, Southern China – Yang et al

“The morbidity of measles shows a seasonal variation. In temperate climates, measles outbreaks typically occur in the late winter and early spring every year, whereas in the tropics, measles outbreaks have irregular associations with rainy seasons, which suggests that climatic factors partly underlie the seasonality of measles virus infections.” – Yang et al

Compare with the epidemiology of influenza:

“Influenza seasonality indicates that New Delhi would likely benefit from springtime vaccination (May–June), whereas vaccination in the fall (October–November) would be better for Srinagar. We recently illustrated that India and most other tropical countries in Asia exhibit influenza seasonality that coincides with the monsoon season, June–October” – Koul et al

The charts from Yang et. al. show an increase in measles cases correlated with:

• Low humidity
• High sunshine
• Moderate temperatures

Other researchers have found correlations with both season and specific local weather events:

“Specific meteorological conditions increased the risk of measles, including lower relative humidity, temperature, and atmospheric pressure; higher wind velocity, sunshine duration, and diurnal temperature variation” – Jia et al

“The team discovered a strong and consistent annual pattern of measles outbreaks that was associated with rainfall. Specifically, they found that the rainy season was associated with a lower risk of measles case reporting, whereas measles cases were higher during the dry season.” – Blake et al

“The analysis revealed that there is a statistically significant relationship between weather parameters (Temperature and Rainfall) and the occurrence of measles in the study area.” – Alhaji et al

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Cosmic events include solar flares, lunar tides, eclipses, strength of Earth’s magnetic field, planetary orbits, planetary alignments and oppositions.

Biological events range from measured chemical reactions to behaviours of individuals include epidemics, admissions to mental hospitals, car accidents, metabolite levels, birth defects, the shape of leaf buds, rate of water uptake in seedlings, blood clotting parameters, blot tests etc.

The brain, nervous system and embryo seem to particularly sensitive to such influences with personalities seemingly affected by the month of conception (more likely than birth date surely?).

A lot of the correlations seem crazy (the thyroid activity of cats is related to the orbit of Mercury for example) and some have been ‘debunked’.

Many researchers tried experiments in Faraday cages or in deep underground caverns. Often some reduction of effect was observed but rarely was it eliminated. Both electric eddy currents and magnetic potential currents seem implicated then with a Faraday cage providing some protection from the former but not the latter.

So what are the causes?

Viral transmission?

Unlikely:

• Attempts to transmit any disease in a clinical trial invariably fail
• Isolation techniques are highly contested
• Computer models need ‘tweaking’ to get plausible results
• The need to add a seasonal factor to models suggests a seasonal influence
• The possibility of extinction events seems too high for virus survival
• The characteristics of the epidemiology seem too structured for random transmission

Poisoning?

Again unlikely: How to explain the epidemiology?

Annual crop spraying or vaccination schedules might just explain how toxin administration is coordinated over a whole country but it isn’t strictly seasonal and ‘drifts’ from year to year. The epidemiology is complex and has patterns that are both local and global.

Cosmic influences?

To most people this will seem the most unlikely of all, but what else is left?

The epidemiology needs explaining and here we at least have a chance of correlating disease with ‘something’ although at the moment it isn’t even clear what that ‘something’ is.

I doesn’t seem credible that the planet Saturn can have a direct influence on biological processes but more likely that various electrical events in the cosmos can and do have an influence and that these phenomena may well correlate with planetary alignments and solar activity.

These patterns, with seasonal variation and local coincidences with weather events are similar to those seen in the epidemiology of influenza. See here: Influenza and weather

Hypothesis

Population wide biological events are triggered by electromagnetic activity as opposed to gravity and that filaments of such energy pervade the solar system, emanate largely from the sun, connect the sun, planets and moons and will move, interact and intertwine as the planets orbit the sun.

If this is true then certain events and patterns are explained that are not expected from gravitational influence alone. Filament interaction will be roughly rhythmic but with various deviations.

We could expect:

• Roughly seasonal effects but with various ‘harmonics’.
• The observed ‘effect’ on Earth may precede the supposed ’cause’ (eg solar flare) because both of these are caused by a third and unsuspected phenomenon.
• ‘Influences’ of two or more planetary orbits may interact in a complicated way.
• Odd phase shifting phenomena may be seen
• Correlations may appear consistent for decades and then disappear, either suddenly or gradually.
• Random and sudden events seemingly unrelated to planetary motion.
• Absent or inverted dose-response relationship (weak stimulus seems to give strong response etc.)
• Relationships which seem outstanding to the eye but disappear upon statistical analysis.

The last above is because it is the wrong things that they are trying to correlate and because the ’causes’ themselves may be only quasi-periodic. The Earth’s rotation speed is not quite constant and solar cycles also vary in length in an unpredictable fashion. Many periodic influences from the solar system are in any case filtered through our ionosphere and weather system which have local rhythms of their own.

All these patterns above are described in the book by J.T. Burns and many are seen in the epidemiology of measles and flu. Many cannot be explained by conventional means so the idea of electromagnetic filaments stands as the most likely explanation for now.

It sounds like almost any pattern of disease outbreak may be possible and that the hypothesis is therefore unfalsifiable. This may well be true at the moment but the hope is that a more detailed understanding of the electromagnetic nature of biology and the electromagnetic activity in the cosmos will some day give something concrete to test against.

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References:

Travelling waves and spatial hierarchies in measles epidemics – Grenfell, Bjornstad
https://www.researchgate.net/publication/11615103_Travelling_waves_and_spatial_hierarchies_in_measles_epidemics

Modelling a modern day pandemic — Developing the SIR model – Benji Tigg
https://medium.com/geekculture/modelling-a-modern-day-pandemic-developing-the-sir-model-8d77599050ce

Influenza Epidemics in the United States, France, and Australia, 1972–1997 – Viboud et. al.
https://wwwnc.cdc.gov/eid/article/10/1/02-0705_article

The State of Measles and Rubella in the WHO European region – Muscat et al
https://pubmed.ncbi.nlm.nih.gov/26580789/

The effects of weather conditions on measles incidence in Guangzhou, Southern China – Yang et al
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4896574/

Estimation of the relationship between meteorological factors and measles using spatiotemporal Bayesian model in Shandong Province, China – Jia et al
https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-023-16350-y

Measles outbreaks in Niger linked to rainfall and temperature, study finds – Blake et al
https://www.sciencedaily.com/releases/2020/08/200825110805.htm

Impact of Climatic Variables on the Prevalence of Measles in Wudil Local Government, Kano State, Nigeria – Aljhaji, Nasir
https://www.irejournals.com/formatedpaper/1701750.pdf

Differences in Influenza Seasonality by Latitude, Northern India – Parvaiz A. Koul et. al.
https://wwwnc.cdc.gov/eid/article/20/10/pdfs/14-0431-combined.pdf

Cosmic influences on humans – JT Burns
https://www.amazon.com/Cosmic-Influences-Humans-Animals-Plants/dp/0810833131

Modelling seasonal measles transmission in China – Bai, Liu
https://www.sciencedirect.com/science/article/abs/pii/S1007570415000088

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Measles again, this time from the WHO – peaking in spring
https://vaxopedia.org/2019/07/08/when-is-measles-season/