The mathematics that explain the end of the pandemic

The United States has already vaccinated more than half of its adults against COVID-19, but it could pass month before the country has vaccinated enough people to achieve herd or group immunity.

And much of the world still desperately awaits access to vaccines.

Meanwhile, countries with rising vaccination rates, such as the United States, can expect a sharp drop in the number of cases.

And sooner than you think.

Indeed, the cases decrease thanks to the principle of exponential decay.

Many of us have learned of the exponential growth in the early days of the pandemic to understand how a small number of cases can quickly turn into a main focus as the chains of transmission multiply.

India, for example, which is embroiled in a major COVID-19 crisis, is in a exponential growth phase.

Exponential growth means the number of cases can double in just a few days.

Exponential decay is what opposite; means that the number of cases can be halved during the same period.

Understanding the exponential dynamics makes it easy to know what to expect in the next phase of the pandemic – why things will improve quickly as vaccination rates rise, and why that matters keep some precautions even after the number of cases decreases.

The exponential decrease will lead to a marked decrease in infections.

All avoided COVID-19 cases have cut the chains of transmission, preventing many more cases in the future.

This means that the same precautions that reduce transmission enough to cause a significant decrease in the number of cases when high translates into a smaller decrease when cases are low.

And these changes add up over time.

For example, Halving 1000 cases each day would mean a reduction of 500 cases on day 1 and 125 cases on day 3, but only 31 cases on day 5.

Therefore, the end of the pandemic may look like this: a sharp drop in cases followed by a longer period of low number of cases, although cases increase again if people relax their precautions too soon.

This trend is already present in the United States: it took just 22 days for daily cases to decrease by 100,000 from the Jan. 8 peak of around 250,000.

But it took more than three times as long for daily cases to decline by another 100,000.

This pattern has also been confirmed among the elderly, who were among the first to gain access to vaccines, and in other countries, such as Israel, where the COVID-19 epidemic is under control.

Infections begin to subside when herd immunity is reached

The main objective is to achieve collective immunity.

Reduces cases to zero by slowing the spread of the virus with a combination vaccination and immunity acquired by infection to maintain the exponential decline even when the company resumes normal operations.

However, contrary to popular belief, achieving group immunity doesn’t prevent all flare-ups, at least not in the beginning.

It just means that there are so few people susceptible to infection that outbreaks that do occur tend to go away and the number of cases goes down.

Over time, the buds each time become less frequent.

It is possible to rapidly reduce the number of COVID-19 cases by exponential decrease, even before group immunity is reached thanks to the vaccination rate.

We just need to maintain the transmission rates of below the inflection point between exponential growth and exponential decrease: when all people with COVID-19 infect less than one person on average.

Anything that people can do to slow the spread goes a long way, including wearing face masks, getting tested, and avoiding crowded indoor spaces, especially in light of concerns about current and future variants as it could cause us lead to overcome. the exponential decay threshold.

As more and more people get vaccinated, people may gradually reduce precautions as cases continue to decline.

Over time, it becomes easier and easier to keep the number of cases low until – and this is what is great about herd or herd immunity based on vaccination – cases can stay that way. almost effortless once enough people are vaccinated.

This is the power of exponential decay.

Cases will rise again if restrictions are lifted too early

However, don’t expect the road to collective immunity to be easy.

It is natural for people to want to decrease precautions when cases are decreasing and to feel reluctant increase them when cases increase again.

The problem is, it can be difficult to know how much precautions need to be reduced while maintaining the downward trend in cases so that the exponential growth does not get out of hand, as it does in India.

Oscillations in the number of cases are less drastic when there are few cases

Fortunately, the exponential dynamics that lead to drastic changes in the number of cases when these are high, make them less marked when there are few cases.

And as more and more people get vaccinated, the swings will also decrease, as fewer people are likely to get it.

Each vaccination helps us stay in the realm of exponential decay.

The same goes for anything people do to slow the spread of the virus, such as wearing masks and social distancing.

The synchronizationn of these efforts amplifies their impact by making the spread of the virus almost impossible and breaking many chains of transmission at once.

The United States is still a long way from obtaining collective immunity, but things could improve much sooner.

The worst of the pandemic may have passed sooner than you think.

Zoë McLaren is an adjunct professor in the School of Public Policy at the University of Maryland in Baltimore County. Study health and economic policies to fight epidemics of infectious diseases, such as HIV, tuberculosis, and COVID-19.

C. 2021 The New York Times Company

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