Spatio--Temporal Population Dynamics for Interacting Species: Vector Control & Predator--Prey

I will present two PDE models for interacting animal species. My first model is for mosquito population control. Mosquitoes top the list of the deadliest animals in the world due to the diseases they carry and transmit to humans, most importantly, malaria. The sterile insect technique (SIT), which entails the periodic mass release of sterilized male mosquitoes into an environment where adult female mosquitoes are abundant, is one of the main promising approaches being proposed to suppress the populations of malaria-spreading mosquitoes. I will use a two-species model of SIT to see how an SIT program can leverage interspecies competition between mosquito species to replace a species of high vectorial capacity with a species of low vectorial capacity. Using this competition, I will show that SIT can locally eradicate malaria-carrying mosquito species at a much lower cost (in terms of the number of sterile males released) than using SIT alone. Second, I will present a PDE model for predator-prey interactions in which the predators' range is a subset of the prey's range. If the predators' range is too large, they may over-hunt the prey whereas if their range is too small, they will not have enough prey available to be able to support a large population. I will show how the existence of nontrivial equilibrium solutions can be proved despite the challenge of having coupled PDEs in different domains, and numerical results showing a rich family of behaviors from solutions of this model. I will address the question of, given a domain for the prey species, what is the subset of that range for the predator species that maximizes the predator population?