# Has NM reached herd immunity?

With 29% of the population vaccinated, New Mexico is No. 1 in the nation in vaccinations. The data from Johns Hopkins University and the CDC can be used to deduce that New Mexico reached the herd immunity threshold on March 16, 2021. Sounds confusing, since the CDC and other experts seem to believe 75% or more vaccinations are needed to reach the herd immunity threshold. Why is this happening?

The simple answer: People and institutions use different models, and so the results differ. We have been overwhelmed with models over the last year, so which one is better? The simple answer is the one yielding results that most accurately match observations. While many choose the most comprehensive models, these can only be solved approximately, leading to vague results. Simple, small models that yield exact solutions are most desirable.

To understand the vaccination discrepancy better, we must go back 94 years when two Englishmen formulated the mother of all epidemic models, the “SIR Model,” that explains how epidemics develop over time. The model is simple, elegant and classic. But there is a catch. The equations are too difficult to solve exactly. But many found approximate solutions that proved wildly popular. According to Google, over 1.5 million research papers have used the model.

A few years ago, we modified the SIR model to use as a forensic tool, designed to identify overpayments in Medicaid programs. Our results were validated implicitly when the state of New Mexico subsequently collected over \$660 million in overpayments. If modifications to the model solved forensic problems, could they shed more light on the epidemic? The answer is yes.

By modifying the equations, we found an exact solution to the SIR model that had eluded scientists for almost a century. And that yielded multiple results subsequently validated by observations. One result in particular was that the threshold for herd immunity — when the epidemic size decreases – starts when the immunized exceeds 25% of the total population.

From the CDC vaccination data and the Johns Hopkins University COVID 19 data, we see that, as of April 6, the epidemic size has decreased in 29 states. New Mexico is the only state on the list that has more than 25% vaccinated, but about a dozen states have reached 25% immunizations by combining the vaccinated and those who have recovered from infection.

Interestingly, while all the states in our list are unaware that they crossed the threshold, Gov. Greg Abbott of Texas has announced Texas is close to the critical point. Experts greeted this optimistic message with much mirth, but when the facts are out, the governor may have the last laugh.

The results and map are available here.

This clearly shows our (25%) result matches observations better.

The onset of herd immunity should be viewed as the start of a journey – when the size of the epidemic begins to decrease, and not as a destination – when the pandemic ends. Many states have large pools of infected people remaining at the onset of herd immunity; without adequate continuing safety measures, the pandemic can easily surge. Infections increase geometrically, in leaps, while recoveries move arithmetically, in small steps. Surges are unavoidable as long as infections remain, and vaccinations will curb them.

The Herd Immunity Map is also a tool for travelers. It offers an opportunity to rate the performance of states in managing the pandemic quantitatively and to identify the least-risky destinations in a geographical region.

Our calculations have not been peer-reviewed but can be found here.

Physmark Inc. and Care Maps Inc. provide software and data modeling services to spot anomalous patterns in health care data. Care Maps shows chronic and cancer disease burdens in various geographical regions, costs for treatments and trends in both disease burdens and costs. The COVID-19 work was based on academic curiosity. Email jkuriyan@att.net.

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