It is extremely important that scientists know the population of insect species in certain areas. Insects play such a huge role in ecosystems and environments. They can be the soul reason an ecosystem is thriving, but they can also be the reason that an ecosystem is failing if they happen to be an invasive species in that area. So knowing the number of insects is very helpful. But it would be impossible to be able to count ever single insect in a given area to get the exact population number. This is where mathematicians come in.
Mathematicians will use complex differential equations to be able to accurately predict and model the population growth and expansion of important species of insects. This helps with the containment of harmful invasive species along with the preservation of the important non invasive species (Dennis 1989).
But what is a differential equation? In mathematics a differential equation is defined as an equation that relates unknown functions and their derivatives. When applied to scenarios, the functions usual represent quantities, the derivatives will represent their rate of change (usual definition of a derivative) and the actual differential equation will define a relationship between the two (Zill 2012).
To model insect population, scientists will analysis data, create a differential equation and plug in values for time and other variables to model the population of certain insect colonies (Dennis 1989).
Solenopsis invicta or red ant/fire ant is an invasive species of ant in the United States that have been studied by scientists for decades. Not only are they a nuisance to humans because of there painful burning sting, they also cause damage to a lot of ecosystem and are very hard to get rid of (Andrew 2024). Mathematicians have kept track of these ants population growth and expansion of decades to be able to predict where they are going to cause damages in the ecosystems.