An Ecoepidemic System With Group Defense And Harvesting

With the increasing demand for biological resources,the role of biological mathematics in biological resource management has received more and more attention.Modeling the dynamics of population interactions is one of the classical problems in ecological science.The combination of population dynamics with disease and human harvest behaviour is more in line with the complex ecological environment and has high research value.Dynamic analysis of a ecoepidemic system with group defense and harvesting are presented in this paper.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 behaviour,while another population is subject to a transmissible disease and behaves individually.By analysing 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.We consider the impact of harvesting on an ecoepidemic model.We have obtained the optimal harvesting strategy,which provides a theoretical basis for humans to maximize the capture of economic benefits.In addition,through numerical simulation,we proved that humans can control the number of diseased individuals in the population through harvesting,so as to achieve the goal of controlling the spread of diseases;the optimal harvesting effort was not only related to external economic conditions.Therefore,we can formulate different harvesting strategies according to different infectious diseases to control the spread of diseases in the population.