An international team of researchers has developed a new mathematical tool that could help scientists to deliver more accurate predictions of how diseases, including COVID-19, spread through towns and cities around the world.

Rebecca Morrison, an assistant professor of computer science at the University of Colorado Boulder, led the research. For years, she has run a repair shop of sorts for mathematical models--those strings of equations and assumptions that scientists use to better understand the world around them, from the trajectory of climate change to how chemicals burn up in an explosion.

As Morrison put it, "My work starts when models start to fail."

She and her colleagues recently set their sights on a new challenge: epidemiological models. What can researchers do, in other words, when their forecasts for the spread of infectious diseases don't match reality? {module INSIDE STORY}

In a study published in the journal Chaos, Morrison and Brazilian mathematician Americo Cunha turned to the 2016 outbreak of the Zika virus as a test case. They report that a new kind of tool called an "embedded discrepancy operator" might be able to help scientists fix models that fall short of their goals--effectively aligning model results with real-world data.

Morrison is quick to point out that her group's findings are specific to Zika. But the team is already trying to adapt their methods to help researchers to get ahead of a second virus, COVID-19.

"I don't think this tool is going to solve any epidemiologic crisis on its own," Morrison said. "But I hope it will be another tool in the arsenal of epidemiologists and modelers moving forward."

When models fail

The study highlights a common issue that modelers face.

"There are very few situations where a model perfectly corresponds with reality. By definition, models are simplified from reality," Morrison said. "In some way or another, all models are wrong."

Cunha, an assistant professor at Rio de Janeiro State University, and his colleagues ran up against that very problem several years ago. They were trying to adopt a common type of disease model--called a Susceptible, Exposed, Infected, or Recovered (SEIR) model--to recreate the Zika virus outbreak from start to finish. In 2015 and 2016, this pathogen ran rampant through Brazil and other parts of the world, causing thousands of cases of severe birth defects in infants.

The problem: No matter what the researchers tried, their results didn't match the recorded number of Zika cases, in some cases miscalculating the number of infected people by tens of thousands.

Such a shortfall isn't uncommon, Cunha said.

"The actions you take today will affect the course of the disease," he said. "But you won't see the results of that action for a week or even a month. This feedback effect is extremely difficult to capture in a model."

Rather than abandon the project, Cunha and Morrison teamed up to see if they could fix the model. Specifically, they asked: If the model wasn't replicating real-world data, could they use that data to fashion a better model?

Enter the embedded discrepancy operator. You can picture this tool, which Morrison first developed to study the physics of combustion, as a sort of spy that sits within the guts of a model. When researchers feed data to the tool, it sees and responds to the information, then rewrites the model's underlying equations to better match reality.

"Sometimes, we don't know the correct equations to use in a model," Cunha said. "The idea behind this tool is to add a correction to our equations."

The method worked. After letting their operator do its thing, Morrison and Cunha discovered that they had nearly eliminated the gap between the model's results and public health records.

Being honest

The team isn't stopping at Zika. Morrison and Cunha are already working to deploy their same strategy to try to improve models of the coronavirus pandemic.

Morrison doubts that any disease model will ever be 100% accurate. But, she said, these tools are still invaluable for informing public health decisions--especially if modelers are upfront about what their results can or can't tell you about a disease.

"This epidemic has revealed how difficult it is to model a real system," Morrison said. "But I hope that people don't take that to mean that we shouldn't trust our scientists."

New supercomputer modeling could play a big part in exit strategies and lifting air travel restrictions

Millions of more people across the EU could have contracted COVID-19 had strict international travel bans not been implemented, shows a new report by supercomputer modeling experts at Stanford University.

Using a newly developed mathematical epidemiology simulation, the study, published in Computer Methods in Biomechanics and Biomedical Engineering, predicts the huge impact that limiting air travel across the 27 EU nations had on restricting the spread of the disease. {module INSIDE STORY}

The simulation can show live estimated figures for the growth of spread for each country if we were to remove travel bans today. The images above show how 0.2% of some populations could have become infected by 20th April (when the study was written, 5 April), however, these figures change daily.

This new model could now play a vital part in establishing politicians' exit strategies, with the team able to virtually lift travel restrictions between individual communities, states, or countries, to explore the potential gradual changes in spreading patterns and outbreak dynamics.

"There is a well-reasoned fear that easing of current (travel restriction) measures, even slightly, could trigger a new outbreak and accelerate the spread to an unmanageable degree," lead author Ellen Kuhl, Professor of Mechanical Engineering at Standford University comments.

"Global network mobility models, combined with local epidemiology models, can provide valuable insight into different exit strategies. Our results demonstrate that mathematical modeling can provide guidelines for political decision making with the ultimate goal to gradually return to normal while keeping the rate of new COVID-19 infections steady and manageable," says Kevin Linka, lead author and a postdoctoral researcher in Dr. Kuhl's group.

From its European origin in Italy, the novel coronavirus spread rapidly via the strongest network connections to Germany, Spain, and France, while slowly reaching the less connected countries, Estonia, Slovakia, and Slovenia.

Currently, the levels of the population known to be infected with the disease vary from country to country, however as of April 18, with the flight being reduced by 89% in Germany, 93% in France, 94% in Italy, and 95% in Spain (Eurostat 2020), the graphs in this study show how the spread has been contained.

"Strikingly, our results suggest that the emerging pattern of the COVID-19 outbreak closely followed global mobility patterns of air passenger travel," confirms Professor Kuhl, whose model can also predict the emerging global diffusion pattern of a pandemic at the early stages of the outbreak.

"Our results suggest that unconstrained mobility would have significantly accelerated the spreading of COVID-19, especially in Central Europe, Spain, and France."

Unfortunately, the model also confirms how travel bans were introduced too late to stop the Europe-wide outbreak altogether.

"A recent study based on a global metapopulation disease transmission model for the COVID-19 outbreak in China has shown that the Wuhan travel ban essentially came too late, at a point where most Chinese cities had already received many infected travelers (Chinazzi et al. 2020). Our study shows a similar trend for Europe, where travel restrictions were only implemented a week after every country had reported cases of COVID-19 (European Centre for Disease Prevention and Control 2020).

"As a natural consequence, unfortunately, no European country was protected from the outbreak," Professor Kuhl, who is the Robert Bosch Chair of Mechanical Engineering at Standford added.

The first official case of COVID-19 in Europe was reported in France on January 24, 2020, followed by Germany and Finland only three and five days later. Within only six weeks, all 27 countries of the European Union were affected, with the last cases reported in Malta, Bulgaria, and Cyprus on March 9, 2020. At this point, there were 13,944 active cases within the European Union and the number of active cases doubled every three to four days (European Centre for Disease Prevention and Control 2020).

Dr. Kuhl adds that although air travel is certainly not the only determinant of the outbreak dynamics, their findings indicate that "mobility is a strong contributor to the global spreading of COVID-19". This is becoming especially important now that many countries are beginning to lift their travel restrictions in an attempt to gradually return to normal.

Other limitations highlighted - like any infectious disease model - include the simulation being subject to data uncertainties from differences in testing, inconsistent diagnostics, incomplete counting, and delayed reporting across all countries.