# IBM researchers use epidemiology to find the best lockdown duration

In a recent paper, we explain a technique to calculate the optimal duration of a periodic lockdown during an outbreak of an infectious disease.

In a recent paper, we explain a technique to calculate the optimal duration of a periodic lockdown during an outbreak of an infectious disease.

COVID-19 has changed our world.

We finally have vaccines, but prevention strategies and mitigation of spread of the virus will stay for the foreseeable future, in the form of lockdowns. While effective for helping to deal with disease spread, the duration of lockdowns during the current pandemic has been typically chosen through empirical observation of symptoms.

But is it the best way?

Our team at IBM Research, in collaboration with the team of Dr. Ira Schwartz at the US Naval Research Laboratory, aims to provide an arguably more accurate approach to the optimal duration of lockdowns, based an epidemiology theory.

In a recent paper, "Optimal periodic closure for minimizing risk in emerging disease outbreaks," published in PLoS One,^{1} we describe a new technique to calculate the optimal duration of a periodic lockdown during an outbreak of an infectious disease where there is no cure or vaccine. Our findings are different from the lockdown durations widely applied during COVID-19.

Using an epidemiological model and a new mathematical formulation, we’ve assessed the optimal duration of a lockdown to help minimize the spread of the virus — and found that it can vary between 10 and 20 days rather than the inflexible and imprecise current protocol of two weeks.

## The rationale of the 14 day duration

During the current pandemic, nations often have imposed lockdowns based on the time it takes for symptoms to appear. This is estimated to be, at most, two weeks. The lockdown would then be periodically reassessed.

However, our findings are different.

We show that an optimal, data-driven way to help control an epidemic is by closing businesses, schools, and other public meeting places for a period roughly equal to two to four times the mean incubation period, or between 10 and 20 days, based on measurable local health factors. After that time, these places can be reopened for about the same period, until the outbreak is controlled and the disease is eradicated.

Importantly, this period depends on the so-called disease reproductive number, or R_{0}, a measure of the potential of the disease to spread in a population. When R₀ is larger than 1, the disease spreads and triggers an outbreak. When R₀ is smaller than 1, the disease dies out after having been put under control.

We’ve found that the higher the value of R₀, the longer the lockdown needs to be to curb the spread, and vice-versa. We’ve also found that when the reproductive number exceeds a certain threshold, the spread cannot be controlled by periodic lockdowns. This observation, which has never been suggested until now, may have important consequences not only for the current COVID-19 pandemic, but also for the next one, whenever it may happen.

## “Control theory” for lockdowns

Not much work has been devoted to the lockdown duration until now. Some recent papers have suggested strategies for lockdowns, but they were mostly computational in nature. Our work, on the other hand, introduces a mathematical framework based on the theory of epidemiology for the assessment of the effect of lockdowns. As such, its application is general and can be used not only for COVID-19, but for any disease for which a periodic shutdown may be necessary to contain and slow community spread.

We used a mathematical approach called control theory, widely used in engineering (for example, for the design of aircrafts and ships), biology and artificial intelligence. We assume that the incidence of the disease — the number of infectious cases per day — is something that can be ‘controlled’ using periodic lockdowns as ‘controllers.’ We then determine the conditions a lockdown needs to meet for the total incidence to be minimized over the course of the outbreak.

Paired with a predictive model, like the one used in IBM Watson Works’ Return to Work Advisor that mixes rigorous epidemiological theory with AI, we believe that our research results can potentially make a difference between a large outbreak and a small one.

It’s clear that to control an outbreak of an infectious disease when there are no vaccinations or treatments, breaking contact is a must. We hope that our work will help to further reduce the contact rate and pave the way to determining an optimal cycle of lockdowns when the next pandemic hits.

## References

- Hindes, J., Bianco, S., & Schwartz, I. B. (2021). Optimal periodic closure for minimizing risk in emerging disease outbreaks. PLOS ONE, 16(1), e0244706.↩