An Ecoepidemic System With Intraspecific Competition And Two Infectious Routes

Ecoepidemic model is a new branch in the field of biological mathematics,which has been a research hotspot for mathematicians.In such models we study the prevalence of disease,but also combine ecological and epidemiological issues simultaneously.Furthermore,the development rule and ecological balance of the population under the influence of diseases are studied.In our work,we study an ecoepidemic model based on mathematical point,and reveal the interaction between infectious disease and population.In this paper,we study an ecoepidemic system with prey group defense,where prey have an emergent carrying capacity and the SI type transmissible disease spreads among the prey in both horizontal and vertical transmissions.First,the existence and stability of all equilibria of the three two-dimensional submodels are studied.We detect that the susceptible prey or infected prey both can live alone eventually.Then,in a three-dimensional ecoepidemic model,we find that proposed system has nine equilibria: three boundary equilibria,three plane equilibria and three interior equilibria.According to the stability of such equilibria,we conclude that predator can be eradicated in the system or disease can be controlled or even eliminated.Moreover,due to the vertical transmission disease and emergent carrying capacity,the susceptible or infected preys can live alone eventually under some constraints.We also conduct the related parameters including the maximal Lyapunov exponent to investigate the stability and direction of Hopf bifurcation.Finally,the numerical analysis is demonstrated to confirm theoretical results.We consider the impact of horizontal and vertical transmissible disease on an ecoepidemic model.The results show that there exist two key parameters,the intrinsic rate of infected prey and the mortality of predator,which play an important role on the dynamics of the system,including the number of interior equilibria,the coexisting populations and the occurrence of bifurcations and bistability.These findings reveal the delicate balance as well as options of sustaining the ecological balance in a complicated ecosystem.In addition,the mechanism of infectious diseases proposed in this paper makes the system possessing more complex and novel dynamical behaviors.