Scientists use mathematical models to describe the natural world

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Researchers from around the U.S. presented their work using mathematics to model natural phenomena and solve some of the greatest challenges on Earth during a seminar on Sunday at this year’s American Association for the Advancement of Science meeting. 

Glenn Webb, a mathematics professor from Vanderbilt University, spoke about his work using simple partial differential equations to model the spread of epidemics. He compared epidemic modeling to hurricane forecasting. He discussed two recent viruses which have made use of epidemic modeling: Zika and influenza. 

In his presentation, Webb spoke of a project recently completed by researchers at Microsoft which sought to track mosquitoes in the Houston area and then use the data to create models of the hypothetical spread of the Zika virus through the Houston area. 

Webb then talked about the influenza virus and its many iterations. While scientists know that flu season coincides with the cold half of the year and that each individual season is associated with a particular strain of the virus, it is not fully known why the virus is only seasonal. According to Webb, what is known is that the virus only has a short duration locally as it exhausts the susceptible population.

On a global scale, such modeling would be helpful in the detection and preparation against a potential pandemic or worldwide epidemic. However, modeling epidemics using partial differential equations can help to show where to take preemptive measures.

Next, Corina Tarnita, an ecology and theoretical biology assistant professor from Princeton University, spoke of using mathematical models to observe vegetation patterns. Her research stems from the use of satellite imagery to observe the locations of vegetation in any given area around the world. According to Tarnita, such images show indications that vegetation spreads through an area in obvious patterns, although this cannot be easily seen from the ground. 

Her research seeks to explain these patterns. One possible explanation, she said, is that the growth of vegetation is induced by water stress. Part of her examination of these patterns led her to researching termites. 

According to Tarnita, termites are excellent engineers and “can accomplish great architectural feats.” Tarnita studied termite colonies of various sizes to see how termite colonies coexist and how that relates to the mounds they form. She found that colonies coexist most effectively when they are of similar sizes and at enough of a distance away from each other. Thus, mounds of termites create a pattern similar to that of the observed vegetation patterns. She described this pattern as hexagonal spacing, with each mound or spot of vegetation having six neighbors around itself. Her research group hopes to further examine the relationship between these two phenomena. 

Lastly, Clint Dawson, a UT-Austin aerospace engineering and engineering mechanics professor and the head of the Institute for Computational Engineering and Science, spoke of his work on modeling shallow water.

Dawson and other researchers use such data to examine storm surges and hurricanes.

Dawson talked about the ADvanced CIRCulation Model, or ADCIRC, which he said proved itself when it did an adequate job of modeling Hurricane Ike. Such models have the ability to show the effects of certain storms and to simulate the effectiveness of protections. In particular, simulations can be used to examine proposals for additional seawalls along Galveston Island and the Bolivar Peninsula, among other potential solutions. 

Speaking more specifically about Hurricane Harvey, the storm came as a surprise, said Dawson. According to him, the storm was not big like Ike and had less time to build. Ultimately, he said, the storm was more of a rainfall event than a surge event. 

Dawson concluded by highlighting some of the pitfalls of these models, such as their inability to include models of sediment erosion, rainfall and runoff, and the need to improve models of nearshore physics. Still, these models are important in decision-making during hurricanes and are used to inform decisions about highway closures and evacuations, among other things.