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Two researchers have devised a method that can be used to forecast outbreaks of dengue–a sometimes fatal mosquito-borne disease–as much as four months in advance.

George Sugihara, a mathematical biologist at Scripps Institution of Oceanography at the University of California San Diego, and mathematician Martin Rypdal at UiT the Arctic University of Norway, found that the size of human populations susceptible to contracting dengue fever during peak seasons of the year can be related to the stability of cases during off-seasons.

“Minor dengue infections occurring in the period between outbreaks contain hidden information about how many people will be susceptible to the infection in the next outbreak,” said Sugihara, who is also a  founding faculty affiliate of the Halıcıoğlu Data Science Institute at UC San Diego. “Being able to predict dengue outbreaks this far in advance has immediate public health significance.”

There are an estimated 390 million human cases of dengue fever worldwide every year. The viral disease prevalent in tropical latitudes produces a range of symptoms including fever, headaches, and a distinctive rash. For most, symptoms disappear after a week but in some cases, dengue can progress to dengue hemorrhagic fever, which can cause severe bleeding and platelet damage. The disease causes the deaths of 10,000 to 20,000 people each year worldwide.

The factors influencing dengue fever outbreaks are numerous and, as Rypdal and Sugihara admit, are practically impossible to measure. Estimating the magnitude of outbreaks through traditional direct measurements requires knowledge of the different immune-types in the local human population, the viral strain that will be active in the next outbreak, the number of mosquitoes, the weather conditions and physical environment that enable mosquitoes to breed, and more. Thus, prediction of outbreaks using traditional measurements is not practical.

But what Rypdal and Sugihara discovered by analyzing the mathematical models used by epidemiologists to simulate the spread of disease was an alternative way to approach the problem that could be practical.

Dengue is a seasonal illness. In cities like San Juan, Puerto Rico, outbreaks occur in the fall and winter. The period from February to September is the “inter-outbreak” off-season. By analyzing properties of models for epidemics, the investigators found a mathematical relationship between how unstable and wildly fluctuating the reported disease occurrences are during the off-season, and the size of the population susceptible to the disease in the ensuing epidemic.

If the off-season is stable (the number of cases does not vary much from week to week), the outbreak the following year is less severe. If the number of off-season cases is unstable (cases vary wildly from week to week or month to month), the magnitude of the ensuing outbreak is much higher. After finding this to be true in models, Rypdal and Sugihara found that a practical measure of stability could be estimated from time series data on the weekly incidence of dengue, and tested it with real-world data from San Juan, Puerto Rico, unique in its long-term and thorough public health records on dengue outbreaks. The pair found that San Juan’s public health statistics over a 25-year period matched what the models predicted would be true – as if, said Sugihara, mathematics itself eliminated the problem posed by the multitude of variables, by creating a single composite proxy for them.

“All this complex machinery gets summarized within the variability of the population during the disease-free period,” he said. “This proxy allows us to decode that.”    

The relationship between the stability in the number of off-season dengue fever cases and the size of the peak season outbreak is a mechanistic association, “meaning that there is a consistent cause and effect connection, which is what makes it potentially a more powerful tool than a mere statistical association where relationships exist without any apparent reason,” said Sugihara.  “Here you actually have a situation where if this variability increases, there is a mechanistic reason to expect an increase in the size of the susceptible population,” he said.

Public health officials could employ the method to prepare for large outbreaks as much as 16 weeks in advance, said Sugihara. This could enable them to take preparatory steps such as ordering adequate supplies of medicines or safeguarding vulnerable populations.

Rypdal and Sugihara suggest that in principle, the idea could apply to other seasonal epidemics such as influenza. They note, however, that it has limits. Although the predicted trend can be seen qualitatively for flu across countries worldwide, because influenza is not as serious as dengue, and flu cases are not consistently reported (or are sometimes misreported as mere colds or other illnesses), the data are not as good and the method should not be as effective.

“The idea requires reliable data as inputs,” said Rypdal.

The study, “Inter-outbreak stability reflects the size of the susceptible pool and forecasts magnitudes of seasonal epidemics,” appears today in the journal Nature Communications, and was supported by the National Science Foundation and the Department of Defense (SERDP).

The paper is among many in which Sugihara has used mathematics to find signals in seemingly random natural events. Sugihara’s early 1990 work on forecasting real-world chaotic systems led him into investment banking in 1996. He worked on questions of systemic risk and on detecting early warning signs of critical transitions during stints with the national banks of several countries. Upon his return to academia in 2002, he focused much of his work on fisheries sustainability and detecting causation in complex data.

Sugihara is the inaugural holder of the McQuown Chair in Natural Science at Scripps. He became interested in the predictability of dengue fever outbreaks after interacting with epidemiologists interested in the applicability of his data-driven approach to their areas of research. Sugihara and Rypdal began collaborating while Rypdal, currently the department head of Mathematics at UiT, was a sabbatical visitor to Scripps in 2017.