Dynamic Analysis of a Population Competition Model with Disease in One Species and Group Defense in Another Species

Abstract

In this paper, we study the dynamics of an ecoepidemic competition system where the individuals of one population gather together in herds with a defensive strategy, showing social behavior, while another predator population is subject to a transmissible disease and behaves individually. By analyzing the existence and stability of the equilibria of the system, we find that the relatively isolated population can be eradicated, or the population with group defense can live alone eventually under some constraints. Infected individuals end up in two possible situations. In the first case, the disease is eventually eliminated, meaning that only healthy and group-defense individuals in the system can survive. In the other case, the spread of the disease is controlled and eventually all three individuals can coexist. We also conduct a correlation analysis using competition parameter and recovery rate of disease as birfurcation parameters in order to study the transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. The long-term dynamics of the boundary and interior equilibria are demonstrated by numerical simulations.