C. What is Herd Immunity?

Herd immunity is the concept that once animals are immune to a particular disease it will provide a means for stopping the spread of that specific contagion. The equation that is applied is:

R = (1-P)Ro

Ro is the reproduction rate.  An Ro of 1 means that the spread will die out due to the limited life span of the virus.  Ro of 2 means that one person will contaminate 2 others, setting in motion a chain-reaction.   

The P in the equation is the immunity of the subject.  This immunity is based on a portion of the population being excluded because of antibodies from a previous exposure or from a successful vaccination.

When Ro = 1 or less that is the herd immunity.   Solving for P for various Ro factors shows the following:

  • Diphtheria  Ro = 6        P = (Ro – 1) / Ro      83%
  • Measles  Ro = 12-18      P = (Ro – 1) / Ro      91% – 94%
  • Influenza  Ro  = 1.6       P = (Ro – 1) / Ro      37.5%
  • COVID-19 Ro  = 5.7       P = (Ro – 1) / Ro      82%

Unfortunately, there are many variables missing from the herd immunity formula.

Firstly, the Ro is based on the number of infections per unit of time.  The number of infections is an empirical determination based on testing.  Testing numbers can be vastly different from the actual number of infections.  As such, Ro is unknown.  And because Ro is unknown, the herd immunity, by definition, cannot be determined. 

Secondly, Ro, and therefor herd immunity, varies depending on location, time, environmental conditions, and demographics.  None of these factors are included in the formula above. 

Using an animal analogy, the herd immunity will depend on whether the cattle are contained within a coral or if they are on the range.  The herd immunity for cattle that are cooped up in a coral may be 85% whereas the herd immunity for cattle on the range may be 20%. In the case of the 20% on the range, the disease will die out before those infected cattle significantly cross paths with uninfected cattle.  Another determining factor could be weather. Many cattle will bunch up to share body heat if it is very cold, thereby increasing the probability of transmission.  Those factors do not exist in the herd immunity equation. 

Thirdly, concurrent causes may contribute to the data if hospitalization or death rates are used as the contagion signal.  However, this skews the data in the opposite direction.  The errors in the infection rates are underestimated, sometimes as much as 8500 percent.  And hospitalizations and deaths will be overestimated, albeit by a much smaller percent.    

Fourthly, there are missing variables.  There is no analysis of a cluster immunity, i.e. where a particular cluster is immune for some reason and the virus transmission dies in that cluster.  

There are numerous flaws when trying to calculate herd immunity:

  • There are climate variables that affect spread, i.e. flu is highest in the winter for both hemispheres.  There is demographic variability, i.e. older people may be more susceptible to one kind of virus.

  • There are health variabilities, i.e. higher contagion in less healthy communities. 

  • There are variabilities in virus mutations, both good and bad.  Many mutations will self-control the spread, but some may take the virus in a more aggressive direction, etc.  

  • There are variabilities in quarantine (sequestering those who are infected).

These are significant variables.  Hence, the current method of determining herd immunity is too flawed to be meaningful. 

Invitation to Nuclear Engineers

 Since it is impossible to measure herd immunity directly, a proxy might be useful.  Proxies are used throughout the scientific world to secure information and data that is impossible to obtain directly. 

The virus spread has an uncanny similarity to a nuclear chain reaction.  One person spreads the virus to multiple people, those people then spread the virus to multiple other people, leading to an exponential growth in virus spread. 

In a nuclear chain reaction, one neutron strikes a uranium atom. It then splits and releases up to 3 more neutrons.  Those neutrons then strike other uranium atoms and so forth.  But, just like the virus, there are complicating factors involved. 

Both viruses and uranium have life spans. And both experiences surges, with nuclear surges exhibited in the form of neutron bursts.

An invitation is extended to all nuclear engineers to investigate whether a mathematical chain reaction model can be applied to viruses.  Or whether a laboratory experiment could be designed that mimics viral propagation.  There is a need to determine Ro, contagiousness, and virus spread models as early as possible.