Scientists have developed a mathematical model to determine whether or not US states are in a “second surge” period of coronavirus infections.
Researchers at the University of Sydney in Australia looked at the data and found that any state with a “second peak” that is less than a fifth of the first is not a true second wave because it is too small.
Using this method, they found that by the end of July at least 31 states such as Florida, Ohio and Pennsylvania were in their second boom.
About 13 states, including California, Texas, and Georgia, had seen infection rates flatten out only slightly and not go down, so they were still in their first waves.
Meanwhile, New York and New Jersey had managed to completely smooth their respective curves, and their first climb was “completely over”
The team says the results can help local and state lawmakers determine when restrictions need to be relaxed by seeing the difference between stable or insufficiently declining infection rates and rates on a downtrend.
Scientists have developed a mathematical model to determine whether or not US states are in a “second surge” period of coronavirus infections. Pictured: The bodies are placed in a refrigerator truck that serves as a temporary morgue outside Wyckoff Hospital during the April 4 coronavirus pandemic in Brooklyn, New York
STILL IN THE FIRST WAVE: Thirteen states including Georgia (left) and California (right) were in their first waves. This is because these states had rising case numbers from January to July with no significant downward movements
NOW IN SECOND WAVE: At least 31 states including Florida (left) and Ohio (right) turned out to be their second waves. These conditions had an initial increase followed by decreasing infections and a second increase
“In some of the worst performing states, policymakers appear to have been looking for a plateau or a slight decrease in infection rates,” said co-author Dr. Nick James, PhD student at the University of Sydney’s School of Mathematics and Statistics.
“Instead, health officials should look for identifiable local maxima and minima that show when the voltage spikes are peaking and when they are demonstrably over.”
For the study, published in the journal Chaos, the team examined data from all 50 US states and the District of Columbia from January 21, 2020 through July 31, 2020.
The researchers adjusted the daily totals to account for low sums that typically occur on weekends and negative counts on the day the counties correct errors.
After the data is smoothed, the mathematical model looks for peaks and valleys and identifies an inflection point.
A turning point has been identified as the trajectory of ascending turns that suddenly sloped down or sharpened downward turns.
Highs and lows must also vary by a certain amount.
For example, a second wave with less than one-fifth the number of cases in the first doesn’t qualify as a second wave because it’s just too small, the researchers say
Thirteen states, including California, Georgia, Mississippi, North Carolina, and Texas, saw rising case numbers over the entire seven-month period.
Because of this, they are considered to be in their first wave with a single increasing attack of infection.
WAVE OVER: New York (left) and New Jersey (right) had managed to smooth their curves after their first wave and were found to have no rise
The researchers assigned the sequence TPTP to 31 states, including Florida, Ohio, and Pennsylvania, which means that no cases were assigned to a first peak, then another trough and another peak.
This means that these states are currently in their second wave. This is an initial increase, followed by a decrease in infections and a second increase.
Meanwhile, New York and New Jersey flattened their respective curves by the end of July and therefore only experienced one wave each.
The remaining four states, Arizona, Utah, Maine, and Vermont, are still affected by their first waves (the former two states) and the second (the latter two states).
“This is not a predictive model,” said James.
“It is an analytical tool designed to help policy makers identify detectable turning points in COVID infections.”
The co-author Dr. Max Menzies, of the Yau Mathematical Sciences Center at Tsinghua University in Beijing, said the analysis shows how reducing constraints when curves are just flattened, not down, can lead to a fatal second rise.
“The real moral of this paper is that COVID-19 is highly contagious and very difficult to control,” he said.
“A real tipping point, where new cases are rightly on the downturn, and not just fluctuating steadily, should be hit before any restrictions are relaxed