Biocontrol of Competing Species with Allee effect

Abstract

Biocontrol of a system relies on the addition of a predator, competitor or parasite to control another species. We develop a model of four autonomous ordinary differential equa- tions with biocontrol of two species of fungus in competition. Both populations have motile and sessile spores with the sessile spores subject to an Allee effect. The one-dimensional sin- gle species model, the two-dimensional competition model, and the two-dimensional single species model, are studied using phase portrait analysis and linear stability analysis to gain insight into how the four dimensional model behaves. The effect of stocking duration, the start time of stocking, and varying initial data on the amount of control agent required to ensure the controlled population survives is explored. We find that by incorporating motile and sessile spores we eliminate any possible trivial equilibriums. Furthermore, applying the control agent sooner results in less being required to ensure the survival of the stocked population.