Risk of Seasonal Super-Exponential Growth of COVID-19

The US and the whole Northern Hemisphere have entered winter, the period when even common colds and flu grow wildly. The daily mortality from COVID-19 increased from <800 per Million in October to >2,500 per Million now. The current situation is more dangerous than it was at the beginning of the pandemic. Some US states and European countries have just experienced episodes of super-exponential COVID-19 growth, and no one knows which area will be next. This article discusses some underlying mechanisms behind this phenomenon. Irrespective of these mechanisms, the time for mass COVID-19 prophylaxis with Hydroxychloroquine is now. The federal government can mail Hydroxychloroquine directly to the people. Anyone who cannot or does not want to use it, could keep it as emergency supplies.

The US COVID-19 case numbers are garbage (the “casedemic”), but the number of deaths are probably accurate within a +/- 30% margin. A lot has been said about comorbidities, but much of what is reported as comorbidities are intermediate causes. Among them are pneumonia (~40%), respiratory failure (36%), ARDS, sepsis, and various cardiac failures [1]. Influenza and pneumonia are reported together, but influenza has almost disappeared because of the extreme social distancing measures.

Basic Reproduction Number & “Herd Immunity”

The effective reproduction number R is a function of pathogen, social behavior, and environmental factors (weather, sunlight, nutrition etc.). The basic reproduction number R0 is defined as R for ordinary social behavior (not including the response to the epidemic) and a certain constant environment. For many infections, environmental factors are constant, because the spread of the infections is either independent of season or happens only in one season. This is not the case with COVID-19. The winter R0 of SARS-COV-2 is higher than for the summer.

Now vs. March 2020

The current COVID-19 situation is a cause for concern. We are currently in a worse situation than we were in March 2020, even with some immune population. Some of the new factors we are facing are:

  • The traditional coronaviruses season is December – April [1b], and we have only entered it.
  • It is believed that the exposure to the common cold beta-coronaviruses (OC43 and HKU1) give people some immune protection against SARS-COV-2. In March 2020, such cross-immunity could be at its peak. However, now we are at least nine months away from such exposure. Extreme social distancing has almost stopped the circulation of common cold coronaviruses.
  • The currently infected population is very large and dispersed
  • Long lockdowns, shutdowns, and other unreasonable restrictions have undermined the population’s innate immunity, which protects against unfamiliar pathogens while the adaptive immune response develops. Some consequences of these restrictions are:
    • Less time spent outside and thus, less exposure to UVB, causing lower levels of vitamin D and AMPs [2]
    • Less physical exercise, which harms immunity [3]
    • Less exposure to bright light interferes with the serotonin-melatonin cycle. Melatonin is thought to have anti-coronavirus properties [4]
    • Long periods of inactivity while being exposed to fear-mongering causes anxiety and stress. Ongoing stress makes us susceptible to illness [5]
    • Shutdowns led to food price increases. At the same time, many people have lost their jobs or other sources of income. This worsens nutrition.

The threshold percentage of immune persons (including antibody and T-cell immunity from earlier infection with the pathogen, cross-immunity, and vaccination) necessary to achieve “herd immunity” is typically computed as 1-1/R0. Most areas of the US are far from the “herd immunity” threshold for  winter.

Super-Exponential Growth

Super-exponential growth was observed near the peak of most seasonal ILI (influenza and influenza-like diseases) in the US [6]. (This paper from the dynamics of complex networks is cited for the data analysis, but not for its hypothesis of the “relational exchange”.) Notice that, on  smaller scales, such effects are even more pronounced. However, when averaged out on a large scale, the effects are harder to detect.

For COVID-19, super-exponential growth happens at the beginning of a new spike, not at the peak. For practical purposes, differences between super-exponential and fast exponential hardly matter.

Here are some fall spikes of COVID-19 observed in the US:

North Dakota – started around October 8, peaked around November 15. 3 times more COVID-19 deaths happened within 10 weeks of this spike than over the whole pandemic period prior to this. That catapulted North Dakota to the 4th place in the COVID-19 mortality (per Million), just after NJ, NY, and MA.

South Dakota – started around October 10, peaked around November 12

Iowa – started around October 26, peaked around November 12

California – started around November 5, still growing

European countries:

Czechia – started around October 2, peaked around October 24

Bulgaria – started around October 5, peaked around November 18

Switzerland – started around October 5, peaked around November 6. COVID-19 mortality in Switzerland jumped 50x, from the daily ~0.2 per Million before the spike to more >10 from November 12,  and still continues to climb.

All these spikes started with super-exponential growth.

Super-Exponential Growth Expression

In the beginning of an epidemic caused by a novel pathogen, the spread is exponential, corresponding to the beginning of the Gompertz curve. But when an infection resurges, like in a second wave, the growth can be faster than exponential. This may happen when the pathogen is already widely spread among the population. The system emerges from the steady state because the pathogen’s effective reproduction number increases over 1. This might happen because of the changing season. Flu and common colds exhibit the same seasonal dynamics.

Exponential growth is (P is the infected proportion of the population; assuming short reproduction times and other parameters like those of SARS-COV-2):

P(t) = P0*exp(R*t), where R is constant

When the effective reproduction number is variable:

P(t) = P0*exp(r(t)*t)

For a short time, In the beginning of a subsequent wave, season-dependent r(t) might be approximated linearly:

r(t) = k*t

P(t) = P0*exp(k*t2)

Super-exponential growth, after a steady state period, can also be caused by changes in social behavior. Denial of access to pharmaceutical prophylaxis and/or early antiviral treatment (Hydroxychloroquine) can also cause such episodes. The latter might be even faster. Government interventions might cause discontinuities in r(t).

Prevention and Treatment Measures

Not only susceptibility to infection, but also the likelihood of a severe outcome might be higher in the winter and during the time of an outbreak. This does not mean that we should hide in burrows like lemmings. It means prevention, early treatment, and special protection of vulnerable populations.

People 45+, who have not had COVID-19, and have no contra-indications, should take HCQ / HCQ + Zinc for prophylaxis (at prophylactic dosage and regimen). In the current situation, when doctors are afraid to prescribe HCQ for COVID-19, it should be available over the counter. Federal government might even ship HCQ, using USPS, to avoid dealing with some state governors.

Other measures for improving respiratory immunity for adults of all ages include vitamin C (0.5-1.0 g/day x3), sunlight, and multi-vitamin/multi-mineral supplements. Ventilation, temperature, and humidity should be increased in buildings where transmission can happen.

In addition, special care should be given to the elderly, to protect them from any contact with potentially contagious COVID-19 carriers. The vaccine is an important development. It is especially suitable for 55+. Nevertheless, we should remember that the emergency approved vaccines have been tested for only a few months, and we should not put all our hopes in them. At the risk of sounding repetitive, it is imperative that sick individuals should be treated early, using an HCQ-based regimen, or something at least equally effective (Ivermectin?).

There is no substitute for acquiring population immunity. The summer was the best time to achieve such immunity among less vulnerable populations (as suggested by Paul Alexander, among others).

The federal government should monitor the spread of SARS-COV-2 and acquired immunity to it, by random sampling for antibodies and T-cells immunity. Media-driven PCR testing is nearly useless. Even the best statistics lag at least five days behind.

No one wants COVID-19 to spread in an uncontrolled or very fast manner. Bursts in COVID-19 infections can be dangerous even for populations which are normally not at risk. This is probably due to high initial viral loads, as was the case in March, among medical personnel. Some measures that were senseless three months ago, do make sense now. Counties, cities, towns, and communities, ruled by governors who do not believe in pharmacological prophylaxis, might want to shut down for a few days, if the number of new symptomatic cases becomes too high.


[1]   Weekly Updates by Select Demographic and Geographic Characteristics, CDC, December 16,  https://www.cdc.gov/nchs/nvss/vsrr/covid_weekly/index.htm#Comorbidities

[1b] What are the seasonal patterns of rhinoviral, coronaviral, enteroviral, and adenoviral upper respiratory tract infections (URIs)? https://www.medscape.com/answers/302460-86798/what-are-the-seasonal-patterns-of-rhinoviral-coronaviral-enteroviral-and-adenoviral-upper-respiratory-tract-infections-uris (accessed December 15, 2020)

[2]   Goldstein L. UVB Activation of AMPs Production in the Skin and the Innate Respiratory Immunity. Watts Up With That? 2020. https://wattsupwiththat.com/2020/11/27/uvb-activation-of-amps-production-in-the-skin-and-the-innate-respiratory-immunity/ (accessed December 15, 2020)

[3]   Nieman DC, Wentz LM. The compelling link between physical activity and the body’s defense system. Journal of Sport and Health Science 2019;8:201–17 https://doi.org/10.1016/j.jshs.2018.09.009

[4]   Shneider A, Kudriavtsev A, Vakhrusheva A. Can melatonin reduce the severity of COVID-19 pandemic? Null 2020;39:153–62. https://doi.org/10.1080/08830185.2020.1756284

[5]   How Stress Affects the Immune System. Psychology Today http://www.psychologytoday.com/blog/how-the-mind-heals-the-body/201411/how-stress-affects-the-immune-system (accessed December 15, 2020)

[6] Scarpino, S., Allard, A. & Hébert-Dufresne, L. The effect of a prudent adaptive behaviour on disease transmission. Nature Phys 12, 1042–1046 (2016). https://doi.org/10.1038/nphys3832

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