Clarkson University Assistant Professor of Mathematics Rana Parshad and his Ph.D. student Emmanul Quansah of Ghana recently published the paper "Biological Control via 'Ecological' Damping: An Approach That Attenuates Non-Target Effects" in the March 2016 volume of Mathematical Biosciences.

The two published the study along with Stephen F. Austin State University's Matthew Beauregard and the University of Georgia's Kelly Black.

They are studying how a mathematical model can be used to create "safe zones" for native species and control the population growth of invasive species.

When an invasive species is introduced to a new habitat, it can harm native species by preying on them or competing for the same resources, enabling the invasive species population to rise to uncontrollable levels -- such as the Burmese python invasion in Florida.

The researchers analyze a mathematical model of biological control to prevent, or minimize, the explosive increase of an invasive species population that functions as a top predator in a three-species food chain.

The study allows for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach uncontrollable population levels in a finite time.

Parshad and Quansah use a partial differential equation model to show that habitat manipulation alone can check the explosive growth of invasive species without any traditional control measures, such as pesticides or the introduction of a natural enemy of the invasive species.

One example of an invasive species population out of control is the cane toad, Quansah said, which was introduced to Australia with the goal of reducing the population of cane beetles responsible for damaging sugar cane crops.

The cane toad did not prey on the cane beetle, and has instead hunted many other native species and disrupted these populations. Some estimates for the current cane toad population surpass 2 billion.

Parshad said a patch, or a safe zone, can be introduced to a habitat to protect a small percentage of the native species, which can then prevent the invasive species from reaching uncontrollable population levels in a finite time.

"This work shows that you don't need to use pesticides or biological controls to prevent the population of invasive species from exploding if you place a patch in the right place," he said.

Quansah said they will continue to study how the size and position of the patch affects the rate of the invasive species population growth. He said depending on the location of the safe zone and how the habitat is manipulated, this method can help control the damage done by invasive populations.

"There is a correlation in the size of the refuge and the rate of the invasive population growth," he said.

Read the full paper at http://www.sciencedirect.com/science/article/pii/S0025556415002722 .