Integrated Pest Management in a Predator-Prey System with Allee Effects

Spatiotemporal dynamics of different growth-diffusion systems on a percolation lattice

To investigate the proliferation and invasion of a tumor within an inhomogeneous matrix, we studied the spatiotemporal dynamics of two types of growth-diffusion systems (GDSs) with logistic or Allee growth occurring on a two-dimensional square site percolation lattice via numerical computation and finite-size scaling approaches. A critical percolation threshold exists in the two systems, but becomes obscure with an increasing Allee effect in Allee growth. The two systems evidently differ in their short-time spatiotemporal patterns: The tumor number density in the logistic model grows and spreads continuously and subdiffusively or weakly superdiffusively while that in the Allee model does so discretely and strongly superdiffusively. This difference is attributed to a lack of cooperation between sites for growth and diffusion in the logistic model as compared to its Allee counterpart. The Allee growth pattern is characterized by a rougher border and more inhomogeneous interior than its logistic counterpart. Judging from their growth-diffusion feature in combination with a clinical image analysis, we conclude that Allee growth is more suitable for modeling the proliferation and invasion of an early-stage malignant tumor than is logistic growth. A phase diagram that correlates a tumor's growth and diffusion on a percolation lattice with a site occupation fraction and Allee effect was established to reveal the sensitivity on proliferation and spreading of a tumor towards the above parameters. The Allee effect was also found to induce diverse dynamic features on its short-time growth and diffusion in the GDS, which brings in an opposite trend toward a tumor's growth and diffusion.

A PREDATOR-PEST MODEL WITH ALLEE EFFECT AND PEST CULLING AND ADDITIONAL FOOD PROVISION TO THE PREDATOR — APPLICATION TO PEST CONTROL

The harmful effects of insect pests on human health and agricultural output are a major global concern. Frequent use of chemical pesticides as a means of pest control can have detrimental effects on the environment, resulting in water and soil pollution, food toxicity, resistance to pesticides, etc. As a result, there is an urgent need to develop a biological pest-control approach that would mitigate these harmful effects. The main purpose of the present study is to explore the interaction between strong Allee effects in the pest with other biological control mechanisms, such as providing additional food to the predator and pest culling as a means of proposing an efficient pest-control policy. To achieve this goal, local stability analysis around the equilibria, possible bifurcation and some basic dynamical features of the system was performed. Our work focuses on the basin of stability in multiple stable regions of the model, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. The system exhibits bi-stability and tri-stability of the equilibria. Our findings indicate that providing additional food to the predator can be an efficient stand-alone pest control strategy, which can, if needed, be combined with other methods.