Ever wonder how herd immunity works? Scientists are just starting to study and aggregate data on the individual differences in how contagious diseases spread. The science is firm on how our immune system works and why outbreaks of diseases eventually fade away. Our immune system is capable of adaptive immunity, which is when it changes to be more sensitive to the unique biochemistry of organisms that invade the body. If an organism is responsible for a disease, the body can mount a stronger and more rapid response with repeated exposures. If the immune system of every individual were sensitized to a disease it would be practically impossible for it to spread and would likely disappear completely, as was the case with smallpox and polio after vaccines became available.

Not every single person has to acquire immunity to prevent the spread of a pathogen. There is a threshold percentage of immunizations over which a disease is unlikely to find enough vulnerable immune systems to spread. The level at which this occurs is called herd immunity. Herd Immunity is dependent on how many people have been immunized against the disease.

## Measuring Exponential Growth

In the study of contagious diseases, the R_{0} (pronounced *R-nought*) of a disease is the number of people each infected person will infect. A person infected with a disease that has a R_{0} of 2, for example, can be expected to infect two other people. A person infected with a disease that has a R_{0} of 10 will infect ten other people. If the R_{0} is greater than one, each infection causes more infections and the disease will spread.

R_{0} is theoretically a single number. However, its calculation is very dependent on human behavior and interaction, so the value varies for different populations in different environments. If calculating the R_{0} for HIV, for example, contagion would be very low or zero for populations that don’t use intravenous drugs or have sex. Similarly, the R_{0} of an airborne virus will be higher in cold regions when people spend more time indoors sharing breathing space.

Most of the time R_{0} is a range, like 12 to 18 for measles or 3.3 to 5.7 for Covid-19. This is because epidemiologists can’t account for all factors in their calculations. The calculation of R_{0} can also be influenced by the number of immunized people in the population. While it is supposed to be defined as the number of secondary infections resulting from each primary infection, it does not take into account the fact that infections leave immunity in their wake, nor is it useful for figuring out how likely a pandemic may be in a given population.

A more accurate method of predicting the formation of a pandemic is the SIR model, or the susceptible, infected, and recovered model. This model involves differential equations to arrive at how the number of infections can influence the rate of infection. One advantage to this model is that it takes into account differences within populations.

The more general and easy to calculate R_{0} is used to define how fast a disease has been spreading, and thus can also be used to define if a disease is slowing down to a point where it will die out.

## Immunization isn’t for everyone

Immunization isn’t practical for every individual in a population. There would be a logistical challenge to ensuring everyone was sufficiently exposed, but more importantly, there are many people whose bodies can’t or won’t acquire immunity. Some people may not be able to make the proper antibodies due to their genetics, and others may have compromised immune systems from other diseases or medical procedures. Fortunately, we can look at the R_{0} of a disease and easily calculate the proportion of immunized people necessary to drop it below 1 and reach herd immunity.

The proportion of immunized people required to reach herd immunity can be found by subtracting one from the inverse of R_{0}. If the disease’s R_{0} is 2, then ½ of the population needs to be immune to bring the effective R_{0} below 1. If the disease’s R_{0} is 5, then four-fifths or 80% of the population needs to be immune. If it’s 10 then nine-tenths need to be immune.

Pathogens evolve, so herd immunity can sometimes fail if a pathogen evolves to exploit a vulnerable subgroup in a population. Herd immunity allows a certain number of “free riders” or individuals who did not get vaccinated or contract the disease. As long as the number of these people remains below one divided by R_{0}, they can ride for free without compromising herd immunity.

In the case of Covid-19, since its R_{0} is somewhere between 3.3 and 5.7, 70% to 82% of the population will need to acquire immunity through either vaccination or infection for the disease to stop spreading according to this model. As of this writing, 69% of Americans plan to get a Covid-19 vaccination and 23% already have, so we are on a good track to stop the pandemic with herd immunity.

However, vaccines are not being distributed equally to everyone. At the current rates, whiter and more wealthy communities will reach herd immunity sooner while those with lower incomes and people of color will be vulnerable for a longer amount of time. You can help by volunteering at vaccination sites in these communities and by encouraging others to do the same. And, of course, talk to your family and your doctor to learn whatever is best for you to help stop the spread of Covid-19.

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